%!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: _kolo.dvi %%Pages: 44 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMR8 CMBX8 CMBX10 CMSY10 CMBX5 LCIRCLEW10 CMR10 CMSY8 %%+ CMBX12 CMMIB10 CMMI10 CMCSC10 CMR9 CMMI9 CMMI7 CMSY7 CMEX10 CMR7 %%+ CMR5 CMMI5 CMSS10 CMSL10 CMTI10 LASY10 CMBX7 CMSY5 CMTI9 CMBX9 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o_kolo.ps _kolo %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2006.03.26:1259 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: psfrag.pro %% %% This is file `psfrag.pro', %% generated with the docstrip utility. %% %% The original source files were: %% %% psfrag.dtx (with options: `filepro') %% %% Copyright (c) 1996 Craig Barratt, Michael C. 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{ kshow } Rif } B /ras { xas { ashow } Rif } B /rs { xs { show } Rif } B /rrs { getrepl dup 2 add -1 roll //restore exec setrepl } B PSfragDict begin islev2 not { /restore { /rrs PSfrag } B } if /show { /rs PSfrag } B /kshow { /rks PSfrag } B /ashow { /ras PSfrag } B /widthshow { /rws PSfrag } B /awidthshow { /raws PSfrag } B end PSfragDict RO pop end %%EndProcSet %%BeginProcSet: f7b6d320.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmb10 cmbx10 cmbx12 cmbx5 cmbx6 cmbx7 cmbx8 cmbx9 cmbxsl10 % cmdunh10 cmr10 cmr12 cmr17cmr6 cmr7 cmr8 cmr9 cmsl10 cmsl12 cmsl8 % cmsl9 cmss10cmss12 cmss17 cmss8 cmss9 cmssbx10 cmssdc10 cmssi10 % cmssi12 cmssi17 cmssi8cmssi9 cmssq8 cmssqi8 cmvtt10 % /TeXf7b6d320Encoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright /numbersign /dollar /percent 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX7 %!PS-AdobeFont-1.1: CMBX7 1.0 %%CreationDate: 1991 Aug 20 16:35:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-55 -250 1289 751}readonly def /UniqueID 5000765 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMIB10 %!PS-AdobeFont-1.1: CMMIB10 1.100 %%CreationDate: 1996 Jul 23 07:54:00 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMIB10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMIB10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -250 1216 750}readonly def /UniqueID 5087392 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: LASY10 %!PS-AdobeFont-1.1: LASY10 1.001 %%CreationDate: 1992 Oct 23 20:19:17 %%RevisionDate: 2001 Jun 05 20:19:17 % Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LASY10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /LASY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 50 /a50 put readonly def /FontBBox{-19 -192 944 683}readonly def /UniqueID 5011949 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSL10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -9.46 def /isFixedPitch false def end readonly def /FontName /CMSL10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-62 -250 1123 750}readonly def /UniqueID 5000798 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9429B9D40924DC059325D9D4CC0344F3F997A99E6CC0676735EBCD685AAC9142 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSS10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMSS10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-61 -250 999 759}readonly def /UniqueID 5000803 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BDCEEA888D07B439DBD4E8B4C9 D198C03874B5E6F8FBF4922065A92BC3E66D05DE53971CB1424510E892442858 D69CE1F76E4DA76C87C763A4B2FE36321E54B1328C9155B8ED6361855A151723 3386AEA3D042B8D89C8C0E9A33E5DF3B466F7BB8C2C8A4ED4CDAFF55FC6D3EE6 0AF2CEBFC1AC3A6E6692F8BB81F82D86BAE85016AD62FCB05467082C2E5AD348 44D1439C2B59F65590E57CA0DE481A7A34E79931B1513C4C30156170409A4BB8 46D412D1DAF88AD30722F12DBCA1CCC6B4BCC28D06B0D29149DDEC520C8FBA13 6B82E2E1790F00B216282FF122EF0D47B70A1B29514DDF7C0435ED238C14BDF5 6DA243117FBEF7398F97EB95597707ED63C6797EBA1B46EA19ABB1DABDA171B3 16CD500F5D64CBFBE4F9CBC3E66A34427D3C4D0C432710289381F9BFD91B4FF4 1E3A896C3EEA2F3105C218877D6C0C6B763760FA364D00065E1CAE9DCB5676ED 286A9ED0D1C946DCA6A2A670EE0936FB4706CC62E234CFEED34AA615C48D2872 A087F30990C85E64BA68F3D5C117123467DB411C9F2D6F6858CC70C1E352C477 713097321B4C4FD4C5CDE305415F998E7245908EEDE6E056A736EA77BD8C639C 3A79FFD0B74B3D28F0494A115F2841CF8A8827AB5608F96FD8998A5F40FB3DFE 3AA0C7696DE4E1D18DC0D6E84B943175FC38FFC42A9C0CBB13A908978C98BFE5 034F88480F32B9DEB2FD228FF6CB0B89B045AB02020C82E3F5716DC640613185 9F597CE262729BC52132F43922B9E28BB71A30AC8709634561B22D13C4FAFE0A 12C4451969226B220038AD8DDA990A4E2CAD53DBEAB698898BBD3046234EB4EA 901287E71CB41296C431383AB85F18882F65BE36923F6C0FD6FADAC5B42FDB68 64C06E047434FA7A659EF7F3E43DB60031885DB8BF7D5F73894B2DE3524B9F39 8345421B8D7D71F3803E9F9CCE8F14F8413FA1A7151004964466F790CDBFDEF4 DF1490966CD3A97C81175BD2D09BC7852FCD02CBDE53369D4D96F09114787F99 D3F0D9A6BE0C339096DAFFE6AE2626200448EBAD5381C6C89D3D8AD93502704C 164CD67734740A76C71478D44CA55148FBB7EAC48E318EE7C3FDB36DB42E5AD6 6AB5480B362D5879069A681AC00317FD810460EF10EF60BEABCEBD64BBF0BDE3 B4202E258DEED04169CDB90CCDCA99702724BBF73F090B294FF383BC1C0E4AA0 983EA528BC64628C4B23B4A0A50431F7D7C25FC7428D1867E75326862F9B1CBE F73B5A687A96C08E347A15FA73A2A55C5650C134FF3C815AC10DD91E0D4829D2 52086B1460858A2ADC19BFCE10417E6F10ED1792FDF699D3BDDBB46455BA96E7 CA45BFD89940198222360BDFB07BF2DB2309 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F D1F017CE45884D76EF2CB9BC5821FD25365DDEA1F9B0FF4CFF25B8E64D0747A3 7CAD14E0DBA3E3CA95F10F24B7D5D75451845F1FB7221D7794A860756CFBB3E7 704A52A22448C34812C3DBEDD41892577AABA7D555E9298C1A0F7DA638078167 F56E29672683C51CF1C003764A8E7AD9D8ADE77B4983F56FE2D12723AAD8BF36 682CFBB71B1D12210144D39DD841A971F71DB82AC6CD815987CDCF29ABC3CC96 5EEBD5D661F452C6E0C74F9ED8D0C5B3755551A172E0FE31EA02344176E32666 14B6853A1C303A5E818C2E455A6CF8FC9A66DC6E279101D61C523BD9DB8EB82F EAF4D7FDF6372383C0794C4568D079648689A199D4B65BA646CF95B7647E4BEC 83856C27A8EF177B3A686EDA6354FE9573E123C12EC4BA56A7E8BFB8F9B75147 9DD79A743968F36F7D0D479FA610F0816E6267E5CE327686A5485AB72201525C FB3B7CA10E1BF26E44C24E1696CB089CB0055BD692C89B237CF269F77A31DC81 0F4B75C8400ABCFDCEC6443CD0E81871CD71AA3064ABDE882C4C52322C27FA8B 41C689F827FB0F8AAF8022CF3C1F41C0B45601190C1328831857CBF9B1E7D1AA 246117E56D6B7938488055F4E63E2A1C8D57C17D213729C68349FEC2C3466F41 171E00413D39DF1F67BC15912F30775AFDF7FB3312587E20A68CF77AD3906040 842D63C45E19278622DD228C18ABDD024DD9613CDC0B109095DB0ADC3A3C0CB5 AB597D490189EA81239E39202CBC7A829EB9B313A8F962F7879D374ADF529BD0 5533EF977142F647AD2F5975BA7E340419116099B19ACCCC37C5512091CC7138 9F339C66B2C9B87906DD509D3C1874AC96FA6F601C45107009B1103B8E6D2CAD 027CC9DF43D33488610180DB2505C0B4944C542FC23B2AA5CED31B5C3AF075D1 B2D97834EFA27989DAC8F6AF46613625E09D8DBD2934051AAA86AD582AE4B226 37325883EF232478F8A08F5F2077C20EE6E67D3819A82650C2C832B39349D523 0C5D7B06B40D81596DB02A06E6B29A9DE51DD7071F5B47F0FE3610DF7EA71A24 11D2F4B88E7AC6025A791B96E59719A0BF6DB4819904C6D73482D981252F0C80 BBFF67D93B2F805D668A6811ACF66552EDDADF695CA09EECA0B8206D67025D84 177779A8FA8860E70EEEC1537885D08284A35C03EE23A0997B5E7C4F0B199F84 11B6A686BFAAD7FD18B2AB4C4365133B89307A9171A145FEDBAE4E581C65E54F 8D6919BBD4E3EE3954D1E18C5575E398A48E03BE67DE9D80BFFB241219B27082 7432078E240A971D973E0F3963635E25BD1EF05019E7E330B2C00E3BB54E7622 C6CD5FA6363888989EBB182A1C553750C88514C9E550AA52A1DA8B3B5A3F10E8 08BFE0A249264E4F93AF4E4BC4FB727D72EFC751A825615FD94C47EE7DC8A612 746361496B1CF543F6868BEB2F0EAD5A85660610268B872D64BBC2E09C020E50 32A38AF70A36D15807F264D810A122918F2CA854834304A2D96296013C3B586C FCC9A35DD1D1DBBF06EA707B3BB325163CC297AB7385D93F443AB1B2203738F2 330D27B7716C20EBE0E1B7458C82C4B14A35107EF40E96ACDA36B0E61456CCA1 13545E3D99DD9BF3D774B3593AC82D35AC285FE827E3D903B0510E52E351672B 876A0BE7BD26E96FD5F6D9102BC326D04311156B2E178639E8DC852A8B9ACBA5 02A714BF2428C8289B4AD1C7A9893132799375077AB4CA0C03A0DF2783725BB0 2036B2EDB1C9BD07D82BF2FBC6C89069DC1FE7A5114D7AAC6AAB566B1F8303CE AA2A75BD34B53103A2B8CF1BF62F1EC7878A90D8E3FF729AFCD1E02DF1E0977B D2B0BF16C4F92339B7B838A191800C7B1035818CE42DA076133EC1F6F05F9BCA E9DF987F2DB7DF1D3596EEB239B3D042ECAEB1CFA47BDD43CF9A74FEFA4420E7 9883817D0481B5DD29F3125EF838 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 80 /summationtext put dup 81 /producttext put dup 82 /integraltext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 104 /bracketleftBig put dup 105 /bracketrightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D251491EBF65A98C9FE2B1CF8D725A70281949 8F4AFFE638BBA6B12386C7F32BA350D62EA218D5B24EE612C2C20F43CD3BFD0D F02B185B692D7B27BEC7290EEFDCF92F95DDEB507068DE0B0B0351E3ECB8E443 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-30 -955 1185 779}readonly def /UniqueID 5000818 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-40 -250 1483 756}readonly def /UniqueID 5000763 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF 5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def /FullName (CMBX8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-59 -250 1235 750}readonly def /UniqueID 5000766 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. 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b(:)g(:)g(:)g(;)g(x)2479 3254 y Fo(k)2520 3242 y Fx(;)g Fs(dy)2641 3254 y Fl(1)2692 3242 y Fs(:)g(:)g(:)g(dy)2887 3254 y Fo(m)2950 3242 y Fx(\))p FA(g)681 3416 y Fx(from)23 b Fs(S)5 b(X)1005 3385 y Fo(k)1069 3416 y Fx(to)24 b Fs(S)5 b FA(X)36 b Fx(suc)n(h)24 b(that)g Fs(P)1743 3385 y Fo(k)1783 3416 y Fx(\()p FB(x)p Fx(;)14 b FA(f)p FB(x)p FA(g)p Fx(\))24 b(=)e(0)i(for)f(all)h FB(x)f FA(2)h(X)12 b Fx(,)25 b(and)f(with)g(the)g (in)n(tensit)n(y)738 3656 y Fs(P)803 3621 y Fo(k)843 3656 y Fx(\()p Fs(x)922 3668 y Fl(1)960 3656 y Fs(;)14 b(:)g(:)g(:)g(;)g(x)1192 3668 y Fo(k)1233 3656 y Fx(\))24 b(=)1376 3543 y Fm(Z)1473 3656 y Fs(P)1538 3621 y Fo(k)1579 3656 y Fx(\()p Fs(x)1658 3668 y Fl(1)1696 3656 y Fs(;)14 b(:)g(:)g(:)f(;)h(x)1927 3668 y Fo(k)1969 3656 y Fx(;)g Fs(d)p FB(y)q Fx(\))24 b(=)2282 3552 y Fn(1)2255 3577 y Fm(X)2243 3753 y Fo(m)p Fl(=0)2400 3543 y Fm(Z)2497 3656 y Fs(P)2562 3621 y Fo(k)2550 3676 y(m)2613 3656 y Fx(\()p Fs(x)2692 3668 y Fl(1)2730 3656 y Fs(;)14 b(:)g(:)g(:)g(;)g (x)2962 3668 y Fo(k)3003 3656 y Fx(;)g Fs(dy)3124 3668 y Fl(1)3175 3656 y Fs(:)g(:)g(:)g(dy)3370 3668 y Fo(m)3433 3656 y Fx(\))p Fs(:)681 3901 y Fx(The)25 b(in)n(tensit)n(y)f(de\014nes) h(the)g(rate)f(of)h(deca)n(y)f(of)h(an)n(y)f(collection)g(of)h Fs(k)j Fx(particles)c Fs(x)3235 3913 y Fl(1)3272 3901 y Fs(;)14 b(:)g(:)g(:)g(;)g(x)3504 3913 y Fo(k)681 4000 y Fx(and)41 b(the)h(measure)f Fs(P)1416 3970 y Fo(k)1457 4000 y Fx(\()p Fs(x)1536 4012 y Fl(1)1574 4000 y Fs(;)14 b(:)g(:)g(:)f(;)h(x)1805 4012 y Fo(k)1846 4000 y Fx(;)g Fs(d)p FB(y)q Fx(\))43 b(de\014nes)f(the)g(distribution)g(of)f(p)r (ossible)g(out-)681 4100 y(comes.)70 b(Supp)r(osing)39 b(that)h(an)n(y)e Fs(k)k Fx(particles)c(from)h(a)g(giv)n(en)f(set)h(of) g Fs(n)j FA(\025)g Fs(k)g Fx(particles)681 4200 y(can)25 b(in)n(teract,)g(w)n(e)g(arriv)n(e)f(to)h(the)h(follo)n(wing)f (generator)e(of)i Fs(k)s Fx(-nary)f(in)n(teracting)h(particles)681 4299 y(de\014ned)j(b)n(y)f(the)h(k)n(ernel)f Fs(P)1535 4269 y Fo(k)1575 4299 y Fx(:)789 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y(initial)28 b Fs(h\027)33 b Fh(with)28 b Fs(h)978 1746 y Fm(R)1033 1813 y Fx(\()p FB(1)19 b Fx(+)f Fs(L)p Fx(\)\()p Fs(x)p Fx(\))p Fs(\027)5 b Fx(\()p Fs(dx)p Fx(\))25 b FA(\024)e Fs(b)1041 2048 y Fi(P)1094 1981 y Fm(\000)1173 2048 y Fx(sup)1132 2122 y Fo(t)p Fn(2)p Fl([0)p Fo(;T)9 b Fl(])1354 2048 y Fs(f)1395 2060 y Fo(L)p Fl(+1)1528 2048 y Fx(\()p Fs(Z)1623 2014 y Fo(h\027)1703 2048 y Fx(\()p Fs(t)p Fx(\)\))24 b Fs(>)f(r)1980 1981 y Fm(\001)2042 2048 y FA(\024)2139 1992 y Fs(C)6 b Fx(\()p Fs(T)h(;)14 b(b;)g(m)2475 2004 y Fl(0)2512 1992 y Fx(\))p 2139 2029 405 4 v 2322 2105 a Fs(r)3059 2048 y Fx(\(4.3\))365 2298 y Fh(for)30 b(all)f Fs(r)h(>)d Fx(0)p Fh(,)j(where)g(the)g(constan)n(t)f Fs(C)6 b Fx(\()p Fs(T)h(;)14 b(b;)g(m)1927 2310 y Fl(0)1964 2298 y Fx(\))30 b Fh(do)r(es)g(not)g(dep)r(end)g(on)g Fs(h)p Fh(;)h(moreo)n(v)n(er,)365 2398 y(suc)n(h)20 b(a)f(family)g Fs(Z)914 2368 y Fo(h\027)994 2398 y Fx(\()p Fs(t)p Fx(\))h Fh(enjo)n(ys)f(the)h(compact)f(con)n 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2986 y Fx(\()p Fs(s)p Fx(\)\()p Fs(dz)2706 2998 y Fl(1)2744 2986 y Fx(\)])p Fs(;)681 3179 y Fx(whic)n(h)31 b(tends)g(to)g(zero)f(as)g Fs(K)k FA(!)29 b(1)i Fx(\(here)g(the)h(assumption)e Fs(\013)f(<)g Fx(1)h(is)h(used\).)48 b(T)-7 b(o)30 b(deal)681 3278 y(with)24 b(the)g(second)g(domain)f(in)h(the)g(same)g(w)n(a)n(y)e(as)i (in)g(the)g(previous)f(theorem,)h(w)n(e)f(need)h(to)681 3378 y(b)r(e)g(sure)f(that)h(not)f(only)g Fs(Z)1522 3348 y Fo(h\027)1602 3378 y Fx(\()p Fs(s)p Fx(\))h(tends)g(to)g Fs(\026)2095 3390 y Fo(s)2154 3378 y Fx(w)n(eakly)-7 b(,)23 b(but)i(also)d(that)i Fs(Z)2991 3348 y Fo(h\027)3071 3378 y Fx(\()p Fs(s)p Fx(\))p Fs(=)p FA(k)p Fs(Z)3321 3348 y Fo(h\027)3400 3378 y Fx(\()p Fs(s)p Fx(\))p FA(k)681 3477 y Fx(tends)j(to)g Fs(\026)1053 3489 y Fo(s)1088 3477 y Fs(=)p FA(k)p Fs(\026)1222 3489 y Fo(s)1257 3477 y FA(k)f Fx(w)n(eakly)-7 b(.)36 b(T)-7 b(o)26 b(see)h(this)g(let)g(us)g (denote)g(b)n(y)f Fs(T)38 b Fx(the)28 b(suprem)n(um)e(o)n(v)n(er)f(all) 681 3577 y Fs(t)34 b 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2801 y Fo(l)1555 2789 y Fx(\)])c(\(1)19 b(+)f Fs(L)p Fx(\()p Fs(y)1930 2801 y Fl(1)1967 2789 y Fx(\)\))2092 2685 y Fo(l)2049 2710 y Fm(Y)2045 2887 y Fo(j)s Fl(=1)2160 2789 y Fx(\()p Fs(h\027)5 b Fx(\()p Fs(dy)2402 2801 y Fo(j)2437 2789 y Fx(\)\))p Fs(:)681 3048 y Fx(Using)27 b(the)h(elemen)n(tary)f(inequalities)1425 3224 y(\()p Fs(a)18 b Fx(+)g Fs(b)p Fx(\))1670 3189 y Fo(\014)1733 3224 y FA(\000)g Fs(a)1860 3189 y Fo(\014)1924 3224 y FA(\000)g Fs(b)2043 3189 y Fo(\014)2110 3224 y FA(\024)23 b Fs(w)2259 3189 y Fl(1)2257 3244 y Fo(\014)2302 3224 y Fx(\()p Fs(ab)2414 3189 y Fo(\014)s Fn(\000)p Fl(1)2562 3224 y Fx(+)18 b Fs(ba)2725 3189 y Fo(\014)s Fn(\000)p Fl(1)2854 3224 y Fx(\))p Fs(;)1316 3363 y(a)p Fx(\(\()p Fs(a)h Fx(+)f Fs(b)p Fx(\))1638 3329 y Fo(\014)1701 3363 y FA(\000)g Fs(a)1828 3329 y Fo(\014)1891 3363 y FA(\000)g Fs(b)2010 3329 y Fo(\014)2055 3363 y Fx(\))23 b FA(\024)g Fs(w)2259 3329 y Fl(2)2257 3384 y Fo(\014)2302 3363 y Fx(\()p Fs(ab)2414 3329 y Fo(\014)2477 3363 y Fx(+)18 b Fs(ba)2640 3329 y Fo(\014)2684 3363 y Fx(\))681 3539 y(\(that)25 b(hold)f(for)g(all)g Fs(\014)j FA(\025)c Fx(1)h(and)g(p)r(ositiv)n(e)g Fs(a;)14 b(b)24 b Fx(with)h(some)e (constan)n(ts)h Fs(w)2954 3509 y Fl(1)2952 3562 y Fo(\014)2997 3539 y Fx(,)h Fs(w)3106 3509 y Fl(2)3104 3562 y Fo(\014)3174 3539 y Fx(dep)r(ending)681 3639 y(only)39 b(on)g Fs(\014)t Fx(,)k(see)c(e.g.)g([7])g(for)g(a)g(pro)r(of)g(of)g(the)h(second)f (one\))g(with)h Fs(a)j Fx(=)f Fs(L)p Fx(\()p Fs(y)3267 3651 y Fl(1)3304 3639 y Fx(\),)h Fs(b)f Fx(=)681 3738 y Fs(L)p Fx(\()p Fs(y)811 3750 y Fl(2)848 3738 y Fx(\))20 b(+)g Fs(:)14 b(:)g(:)20 b Fx(+)g Fs(L)p Fx(\()p Fs(y)1317 3750 y Fo(l)1342 3738 y Fx(\),)32 b(and)e(again)g(the)g(symmetry)g (yields)h(for)f(the)h(last)f(expression)f(the)681 3838 y(estimate)1337 3895 y Fo(k)1295 3920 y Fm(X)1303 4098 y Fo(l)p Fl(=2)1429 3999 y Fs(\024)1477 3964 y Fo(l)1477 4019 y(\014)1522 3999 y Fx(\()p Fs(L)1611 3964 y Fo(\014)1655 3999 y Fx(\()p Fs(y)1728 4011 y Fl(1)1766 3999 y Fx(\))18 b(+)g Fs(L)1956 3964 y Fo(\014)s Fn(\000)p Fl(1)2086 3999 y Fx(\()p Fs(y)2159 4011 y Fl(1)2196 3999 y Fx(\)\))p Fs(L)p Fx(\()p Fs(y)2390 4011 y Fl(2)2427 3999 y Fx(\))2520 3895 y Fo(l)2478 3920 y Fm(Y)2473 4096 y Fo(j)s Fl(=1)2588 3999 y Fx(\()p Fs(h\027)5 b Fx(\()p Fs(dy)2830 4011 y Fo(j)2866 3999 y Fx(\)\))403 b(\(4.18\))681 4247 y(with)28 b(some)f(constan)n(ts)f Fs(\024)1493 4217 y Fo(l)1493 4271 y(\014)1538 4247 y Fx(.)37 b(In)27 b(case)g Fs(k)f(>)d Fx(2,)k(this)h(do)r(es)f(not)g(exceed)h(~)-43 b Fs(af)2972 4264 y Fo(L)3018 4247 y Fj(\014)10 b Fx(\()p Fs(h\027)5 b Fx(\))19 b(+)3317 4225 y(~)3320 4247 y Fs(b)28 b Fx(with)681 4368 y(some)k(~)-43 b Fs(a;)971 4346 y Fx(~)974 4368 y Fs(b)o Fx(,)33 b(as)e(b)n(y)g(\(ND)1448 4332 y Fn(0)1472 4368 y Fx(\))h(the)g(b)r(oundedness)f(of)h Fs(f)2314 4380 y Fo(L)2363 4368 y Fx(\()p Fs(h\027)5 b Fx(\))33 b(implies)f(the)g(b)r(oundedness)f(of)681 4467 y Fs(f)722 4479 y Fd(1)763 4467 y Fx(\()p Fs(h\027)5 b Fx(\).)43 b(F)-7 b(rom)29 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5187 y Fl(+)3405 5217 y Fx(\()p Fs(X)7 b Fx(\))p eop end %%Page: 123 29 TeXDict begin 123 28 bop 365 725 a Fq(Kinetic)26 b(equations)g(for)g (jump-t)n(yp)r(e)f(in)n(teractions)1257 b(123)365 1016 y Fh(and)27 b(that)g(the)h(initial)f(conditions)g Fs(h\027)32 b Fh(are)26 b(suc)n(h)g(that)2109 949 y Fm(R)2164 1016 y Fx(\()p Fs(L)2253 986 y Fo(\014)2298 1016 y Fx(\)\()p Fs(x)p Fx(\))p Fs(h\027)5 b Fx(\()p Fs(dx)p Fx(\))25 b FA(\024)e Fs(C)33 b Fh(for)27 b(all)f Fs(h\027)365 1116 y Fh(and)35 b(some)g Fs(C)42 b(>)35 b Fx(0)g Fh(and)g(an)g(in)n (teger)g Fs(\014)40 b(>)35 b Fx(1)p Fh(,)i(the)e(transition)g(k)n (ernel)f Fs(P)47 b Fh(is)36 b Fx(\(1)23 b(+)g Fs(L)p Fx(\))3147 1085 y Fl(+)3202 1116 y Fh(-)365 1215 y(b)r(ounded,)28 b(is)g Fs(L)p Fh(-non-increasing)d(and)i Fx(\(ND)1764 1179 y Fn(0)1787 1215 y Fx(\))h Fh(holds.)490 1315 y(Then)36 b(there)h(is)f(a)g(subsequence)g(of)g(the)h(family)f(of)h(pro)r(cesses) d Fs(Z)2636 1285 y Fo(h\027)2716 1315 y Fx(\()p Fs(t)p Fx(\))j 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Fx(;)i FB(z)p Fx(;)g Fs(d)p FB(y)q Fx(\))p Fs(\026)2727 4695 y Fl(~)2718 4706 y Fn(\012)2718 4760 y Fo(s)2776 4740 y Fx(\()p Fs(d)p FB(z)p Fx(\))1641 4958 y FA(\024)1728 4845 y Fm(Z)1811 4958 y Fx(\()p Fs(L)1900 4923 y Fo(\014)s Fn(\000)p Fo(\013)2040 4958 y Fx(\))2072 4923 y Fl(+)2127 4958 y Fx(\()p FB(z)p Fx(\)\()p FB(1)20 b Fx(+)e Fs(L)2473 4923 y Fo(\013)2520 4958 y Fx(\))2552 4923 y Fl(+)2607 4958 y Fx(\()p FB(z)p Fx(\))p Fs(\026)2772 4912 y Fl(~)2763 4923 y Fn(\012)2763 4978 y Fo(s)2820 4958 y Fx(\()p Fs(d)p FB(z)p Fx(\))365 5183 y(when)28 b(passing)f(to)g(the)h(limit)g(on)g(b)r (oth)g(sides)f(of)h(\(4.9\).)p eop end %%Page: 126 32 TeXDict begin 126 31 bop 681 725 a Fq(126)2174 b(V.N.)25 b(Kolok)n(oltso)n(v)805 1016 y Fx(\(ii\))g(It)f(follo)n(ws)f(directly)g (from)g(\(4.9\))h(that)g(the)g(function)2616 949 y Fm(R)2685 1016 y Fs(g)s Fx(\()p Fs(x)p Fx(\))p Fs(\026)2889 1028 y Fo(t)2919 1016 y Fx(\()p Fs(dx)p Fx(\))h(is)f(absolutely)681 1116 y(con)n(tin)n(uous)34 b(for)h(an)n(y)f Fs(g)k Fx(from)d(\(i\).)61 b(The)35 b(required)f(con)n(tin)n(uit)n(y)h(for)g(more)f(general)g Fs(g)k Fx(is)681 1215 y(obtained)28 b(again)f(b)n(y)h(appro)n(ximating) e(these)i Fs(g)j Fx(b)n(y)d(functions)g(with)h(a)f(compact)f(supp)r (ort)681 1315 y(using)c(the)i(observ)-5 b(ation)22 b(that)j(the)f(in)n (tegrals)f(of)h Fs(g)i Fx(and)e(its)h(appro)n(ximations)c(o)n(v)n(er)i (the)h(set)681 1414 y FA(f)p Fs(x)g Fx(:)h Fs(L)p Fx(\()p Fs(x)p Fx(\))g FA(\025)f Fs(K)6 b FA(g)27 b Fx(can)i(b)r(e)f(made)h (uniformly)f(arbitrary)e(small)i(for)g(all)h Fs(\026)3006 1426 y Fo(t)3035 1414 y Fx(,)g Fs(t)24 b FA(2)h Fx([0)p Fs(;)14 b(T)e Fx(],)27 b(b)n(y)681 1514 y(c)n(ho)r(osing)f Fs(K)33 b Fx(large)26 b(enough.)805 1614 y(\(iii\))31 b(F)-7 b(or)29 b Fs(g)j Fx(from)d(\(i\),)i(equation)e(\(3.10\))g(holds) g(almost)g(ev)n(erywhere,)g(whic)n(h)g(follo)n(ws)681 1713 y(from)e(\(4.9\).)37 b(But)28 b(as)e(it)i(follo)n(ws)f(from)g (\(ii\),)i(the)f(in)n(tegral)1644 1860 y Fm(Z)1741 1973 y Fs(\036)p Fx(\()p 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Fx(b)n(y)e(pro)r(ducts,)681 2843 y(and)34 b(outside)g(this)h (domain)e(all)h(in)n(tegrals)f(are)g(uniformly)i(small\).)56 b(Consequen)n(tly)34 b(the)681 2943 y(r.h.s.)27 b(of)h(\(3.10\))e(is)i (con)n(tin)n(uous,)f(whic)n(h)g(implies)h(the)g(claim)f(in)h(\(iii\).) 805 3042 y(\(iv\))39 b(Cho)r(osing)f Fs(g)j Fx(to)d(b)r(e)h(c)n (haracteristic)d(functions)j(of)g(Borel)e(sets,)k(w)n(e)d(get)g (\(3.7\))681 3142 y(set-wise.)e(As)1196 3342 y FA(k)p Fs(\026)1288 3354 y Fo(t)1335 3342 y FA(\000)18 b Fs(\026)1468 3354 y Fo(s)1503 3342 y FA(k)23 b Fx(=)66 b(sup)1656 3415 y Fo(g)r Fl(:)p Fn(j)p Fo(g)r Fn(j\024)p Fl(1)1882 3229 y Fm(Z)1978 3342 y Fs(g)s Fx(\()p Fs(x)p Fx(\)\()p Fs(\026)2214 3354 y Fo(t)2263 3342 y FA(\000)18 b Fs(\026)2396 3354 y Fo(s)2431 3342 y Fx(\)\()p Fs(dx)p Fx(\))25 b(=)e Fs(O)r Fx(\()p Fs(t)c FA(\000)f Fs(s)p Fx(\))681 3587 y(uniformly)30 b(for)f(0)e FA(\024)g Fs(s)g FA(\024)g Fs(t)g FA(\024)g Fs(T)41 b Fx(with)30 b(an)g(arbitrary)e Fs(T)12 b Fx(,)30 b(w)n(e)g(conclude)g(that)g FA(k)p Fs(\026)3271 3599 y Fo(t)3300 3587 y FA(k)f Fx(is)h(an)681 3687 y(absolutely)23 b(con)n(tin)n(uous)f(function)j(of)e Fs(t)h Fx(in)g(the)g(sense)g(of)f(the)h(norm)g(top)r(ology)e(on)h FA(M)p Fx(\()p Fs(X)7 b Fx(\).)681 3786 y(By)22 b(the)g(ab)r(o)n(v)n(e) f(reasoning)f(w)n(e)i(conclude)g(that)h(the)f(norm)g(con)n(tin)n(uit)n (y)g(of)g(the)h(map)f Fs(t)h FA(7!)g Fs(\026)3516 3798 y Fo(t)681 3886 y Fx(implies)29 b(the)h(norm)e(con)n(tin)n(uit)n(y)h (of)g(the)h(map)f Fs(t)c FA(7!)h Fs(L)2369 3856 y Fo(\013)2416 3886 y Fx(\()p Fs(x)p Fx(\))p Fs(\026)2577 3898 y Fo(t)2607 3886 y Fx(\()p Fs(dx)p Fx(\),)31 b(whic)n(h)e(together)g(with)681 3986 y(\(4.22\))f(implies)g(the)h(norm)f(con)n(tin)n(uit)n(y)g(of)h (the)g(r.h.s.)f(of)h(\(3.7\).)39 b(T)-7 b(o)28 b(complete)h(the)g(pro)r (of)681 4085 y(of)34 b(the)g(theorem,)i(it)e(remains)g(to)g(notice)g (that)g(if)51 b(_)-39 b Fs(\026)2370 4097 y Fo(t)2433 4085 y Fx(=)34 b Fs(\027)2573 4097 y Fo(t)2636 4085 y 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b(exists)h(a)f(unique)h(non-negativ)n(e)e(solution)h Fs(\026)2291 4890 y Fo(t)2344 4878 y Fh(to)h Fx(\(3.10\))e(\()p Fh(and)i(similarly)f(to)h Fx(\(3.22\)\))681 4978 y Fh(satisfying)j Fx(\(4.19\))g Fh(and)g(a)g(giv)n(en)g(initial)h(condition)f Fs(\026)2392 4990 y Fl(0)2457 4978 y Fh(suc)n(h)g(that)1631 5074 y Fm(Z)1714 5187 y Fx(\(1)19 b(+)f Fs(L)1947 5153 y Fo(\014)1991 5187 y Fx(\)\()p Fs(x)p Fx(\))p Fs(\026)2184 5199 y Fl(0)2222 5187 y Fx(\()p Fs(dx)p Fx(\))25 b Fs(<)d FA(1)p Fs(:)p eop end %%Page: 129 35 TeXDict begin 129 34 bop 365 725 a Fq(Kinetic)26 b(equations)g(for)g (jump-t)n(yp)r(e)f(in)n(teractions)1257 b(129)365 1016 y Fh(This)24 b Fs(\026)601 1028 y Fo(t)654 1016 y Fh(is)f(a)g(strong)g (solution)g(of)g(the)h(corresp)r(onding)e(kinetic)i(equation,)g(i.e.)f (it)h(satis\014es)365 1116 y Fx(\(3.7\))39 b(\()p Fh(or)f(the)i (corresp)r(onding)d(strong)h(analog)f(of)i Fx(\(3.22\)\))p Fh(,)j(where)c(the)i(deriv)-5 b(ativ)n(e)38 b(is)365 1215 y(understo)r(o)r(d)28 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b(w)n(e)g(shall)365 2654 y(consider)29 b(only)g(equation)g(\(3.10\),)g(as)g(\(3.22\))g(can) g(b)r(e)h(e\013ectiv)n(ely)f(included)h(in)g(this)f(case)365 2754 y(due)42 b(to)f(the)h(a)e(priori)h(lo)n(w)n(er)e(b)r(ounds)j(on)f (the)g(solutions)g(obtained)g(in)g(the)h(pro)r(of)f(of)365 2854 y(Theorem)35 b(4.2.)62 b(As)36 b(b)n(y)g(Theorem)f(4.2)g(\(iv\),)k Fs(\026)1915 2866 y Fo(t)1980 2854 y Fx(and)d Fs(\027)2191 2866 y Fo(t)2256 2854 y Fx(are)f(solutions)g(of)h(\(3.7\))g(with)365 2953 y(con)n(tin)n(uous)21 b(righ)n(t)f(hand)i(sides,)g(Lemma)f(A)h (from)f(the)g(App)r(endix)i(\(see)e(also)f(remark)g(after)365 3053 y(this)g(lemma\))g(can)f(b)r(e)h(applied)g(to)f(the)h(measure)f (\(1)r(+)r Fs(L)p Fx(\)\()p Fs(x)p Fx(\)\()p Fs(\026)2312 3065 y Fo(t)2344 3053 y FA(\000)r Fs(\027)2452 3065 y Fo(t)2482 3053 y Fx(\)\()p Fs(dx)p Fx(\).)35 b(Consequen)n(tly)-7 b(,)365 3153 y(denoting)27 b(b)n(y)g Fs(f)862 3165 y Fo(t)919 3153 y Fx(a)f(v)n(ersion)g(of)h(the)h(densit)n(y)f(of)h Fs(\026)1937 3165 y 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FA(k)p Fs(\026)1253 3079 y Fo(t)1281 3067 y FA(k)p Fx(.)44 b(Hence)30 b(from)f(no)n(w)g(on) h(w)n(e)f(shall)h(consider)f(only)g(the)h(limits)h Fs(t)26 b FA(!)h Fs(s)681 3167 y Fx(with)h Fs(t)23 b FA(\025)g Fs(s)p Fx(.)805 3266 y Fh(Step)28 b Fx(2.)p 805 3296 V 28 w(F)-7 b(or)27 b(an)h(arbitrary)d(measurable)i Fs(A)d FA(\032)f Fs(Y)46 b Fx(and)28 b(an)f(arbitrary)f(represen)n(tativ)n(e) 681 3366 y Fs(\033)728 3378 y Fo(t)785 3366 y Fx(of)i(the)g(densit)n(y) -7 b(,)27 b(w)n(e)g(ha)n(v)n(e)963 3581 y Fs(O)r Fx(\()p Fs(t)19 b FA(\000)f Fs(s)p Fx(\))24 b(=)1374 3468 y Fm(Z)1372 3706 y Fo(A)1471 3581 y FA(j)p Fs(\026)1544 3593 y Fo(t)1574 3581 y FA(j)p Fx(\()p Fs(dy)s Fx(\))19 b FA(\000)1850 3468 y Fm(Z)1848 3706 y Fo(A)1946 3581 y FA(j)p Fs(\026)2019 3593 y Fo(s)2055 3581 y FA(j)p Fx(\()p Fs(dy)s Fx(\))24 b(=)2340 3468 y Fm(Z)2338 3706 y Fo(A)2437 3581 y Fs(\033)2484 3593 y Fo(t)2514 3581 y Fs(\026)2564 3593 y Fo(t)2593 3581 y Fx(\()p Fs(dy)s Fx(\))19 b FA(\000)2846 3468 y Fm(Z)2844 3706 y Fo(A)2943 3581 y Fs(\033)2990 3593 y Fo(s)3026 3581 y Fs(\026)3076 3593 y Fo(s)3111 3581 y Fx(\()p Fs(dy)s Fx(\))1287 3861 y(=)1374 3748 y Fm(Z)1372 3986 y Fo(A)1457 3861 y Fx(\()p Fs(\033)1536 3873 y Fo(t)1585 3861 y FA(\000)f Fs(\033)1715 3873 y Fo(s)1751 3861 y Fx(\))p Fs(\026)1833 3873 y Fo(s)1869 3861 y Fx(\()p Fs(dy)s Fx(\))g(+)2121 3748 y Fm(Z)2120 3986 y Fo(A)2218 3861 y Fs(\033)2265 3873 y Fo(t)2295 3861 y Fx(\()p Fs(\026)2377 3873 y Fo(t)2425 3861 y FA(\000)g Fs(\026)2558 3873 y Fo(s)2594 3861 y Fx(\)\()p Fs(dy)s Fx(\))p Fs(:)681 4143 y Fx(As)23 b(the)g(second)f(term)h(here)f(is)h(also)f(of)g(order)g Fs(O)r Fx(\()p Fs(t)9 b FA(\000)g Fs(s)p Fx(\),)24 b(w)n(e)f(conclude)f (that)h(the)h(\014rst)e(term)681 4242 y(is)30 b(of)h(order)e Fs(O)r Fx(\()p Fs(t)21 b FA(\000)f Fs(s)p Fx(\))31 b(uniformly)f(for)g (all)g Fs(A)h Fx(and)f Fs(s;)14 b(t)p Fx(.)46 b(Hence)30 b Fs(\033)2777 4254 y Fo(t)2835 4242 y FA(!)e Fs(\033)2993 4254 y Fo(s)3059 4242 y Fx(almost)i(surely)681 4342 y(with)d(resp)r (ect)f(to)g FA(j)p Fs(\026)1325 4354 y Fo(s)1360 4342 y FA(j)h Fx(as)e Fs(t)e FA(!)g Fs(s)p Fx(.)37 b(As)26 b Fs(\033)1936 4354 y Fo(t)1992 4342 y Fx(tak)n(es)f(only)h(three)g(v) -5 b(alues)26 b(\(0)p Fs(;)14 b Fx(1)p Fs(;)g FA(\000)p Fx(1\),)25 b(it)i(follo)n(ws)681 4442 y(that)41 b(_)-36 b Fs(\033)908 4454 y Fo(s)944 4442 y Fx(\()p Fs(x)p Fx(\))28 b(exists)g(and)f(v)-5 b(anishes)27 b(for)g(almost)g(all)g Fs(x)i Fx(with)f(resp)r(ect)f(to)g FA(j)p Fs(\026)3033 4454 y Fo(s)3069 4442 y FA(j)p Fx(.)681 4619 y Fg(R)l(emark)j Fx(A.1.)41 b(W)-7 b(riting)28 b(no)n(w)f(formally)1189 4779 y Fs(d)p 1174 4816 74 4 v 1174 4892 a(dt)1257 4835 y FA(k)p Fs(\026)1349 4847 y Fo(t)1378 4835 y FA(k)22 b Fx(=)1555 4779 y Fs(d)p 1540 4816 V 1540 4892 a(dt)1637 4722 y Fm(Z)1633 4960 y Fo(Y)1734 4835 y Fs(\033)1781 4847 y Fo(t)1810 4835 y Fs(\026)1860 4847 y Fo(t)1890 4835 y Fx(\()p Fs(dy)s Fx(\))h(=)2152 4722 y Fm(Z)2148 4960 y Fo(Y)2262 4835 y Fx(_)-36 b Fs(\033)2296 4847 y Fo(t)2325 4835 y Fs(\026)2375 4847 y Fo(t)2405 4835 y Fx(\()p Fs(dy)s Fx(\))19 b(+)2658 4722 y Fm(Z)2654 4960 y Fo(Y)2754 4835 y Fs(\033)2801 4847 y Fo(t)2847 4835 y Fx(_)-39 b Fs(\026)2881 4847 y Fo(t)2910 4835 y Fx(\()p Fs(dy)s Fx(\))681 5117 y(and)22 b(noticing)g(that)g(the)g (\014rst)g(term)g(here)g(v)-5 b(anishes)22 b(\(b)n(y)g(Step)h(2\))f (yields)f(\(A.1\).)36 b(Ho)n(w)n(ev)n(er,)681 5217 y(this)28 b(formal)f(calculation)f(can)h(not)h(b)r(e)g(justi\014ed)g(for)g(an)f (arbitrary)e(c)n(hoice)i(of)h Fs(\033)3237 5229 y Fo(t)3266 5217 y Fx(.)p eop end %%Page: 133 39 TeXDict begin 133 38 bop 365 725 a Fq(Kinetic)26 b(equations)g(for)g (jump-t)n(yp)r(e)f(in)n(teractions)1257 b(133)490 1016 y Fh(Step)28 b Fx(3.)p 490 1045 254 4 v 39 w(Let)40 b(us)f(c)n(ho)r (ose)g(no)n(w)g(an)g(appropriate)f(represen)n(tativ)n(e)f(of)j Fs(\033)2809 1028 y Fo(t)2839 1016 y Fx(.)72 b(F)-7 b(or)39 b(this)365 1116 y(purp)r(ose)d(let)i(us)e(p)r(erform)h(the)g(Leb)r (esgue)f(decomp)r(osition)g(of)h Fs(\027)2476 1128 y Fo(t)2542 1116 y Fx(in)n(to)f(the)i(sum)e Fs(\027)3097 1128 y Fo(t)3165 1116 y Fx(=)365 1215 y Fs(\027)411 1185 y Fo(s)406 1236 y(t)460 1215 y Fx(+)13 b Fs(\027)584 1185 y Fo(a)579 1236 y(t)649 1215 y Fx(of)24 b(a)h(singular)e(and)i(an) f(absolutely)g(con)n(tin)n(uous)g(measure)g(with)h(resp)r(ect)f(to)h FA(j)p Fs(\026)3154 1227 y Fo(t)3183 1215 y FA(j)p Fx(.)365 1315 y(Let)30 b Fs(\021)557 1327 y Fo(t)615 1315 y Fx(b)r(e)g(the)g (densit)n(y)f(of)g Fs(\027)1305 1285 y Fo(s)1300 1335 y(t)1370 1315 y Fx(with)h(resp)r(ect)f(to)g(its)g(total)g(v)-5 b(ariation)29 b(measure)f FA(j)p Fs(\027)3012 1285 y Fo(s)3007 1335 y(t)3048 1315 y FA(j)p Fx(,)h(i.e.)365 1414 y(the)35 b(class)e(of)h(functions)g(taking)g(v)-5 b(alues)34 b(0)p Fs(;)14 b Fx(1)p Fs(;)g FA(\000)p Fx(1)32 b(and)i(suc)n(h)f(that)i Fs(\027)2589 1384 y Fo(s)2584 1435 y(t)2658 1414 y Fx(=)f Fs(\021)2798 1426 y Fo(t)2827 1414 y FA(j)p Fs(\027)2896 1384 y Fo(s)2891 1435 y(t)2932 1414 y FA(j)g Fx(almost)365 1514 y(surely)21 b(with)h(resp)r(ect)f(to)h FA(j)p Fs(\027)1228 1484 y Fo(s)1223 1535 y(t)1263 1514 y FA(j)p Fx(.)35 b(No)n(w)21 b(let)h(us)g(pic)n(k)f(up)g(an)h Fs(f)2175 1526 y Fo(t)2225 1514 y Fx(from)f(the)h(in)n(tersection)f Fs(\033)3039 1526 y Fo(t)3075 1514 y FA(\\)6 b Fs(\021)3177 1526 y Fo(t)3206 1514 y Fx(,)365 1614 y(i.e.)31 b Fs(f)40 b Fx(is)31 b(a)g(represen)n(tativ)n(e)e(of)i(b)r(oth)g(densit)n(y)g (classes)f(sim)n(ultaneously)-7 b(.)46 b(Suc)n(h)31 b(a)f(c)n(hoice)365 1713 y(is)f(p)r(ossible,)f(b)r(ecause)g Fs(\026)1144 1725 y Fo(t)1201 1713 y Fx(and)h Fs(\027)1410 1683 y Fo(s)1405 1734 y(t)1474 1713 y Fx(are)e(m)n(utually)h(singular.)38 b(F)-7 b(rom)28 b(this)h(de\014nition)f(of)h Fs(f)3201 1725 y Fo(t)365 1813 y Fx(and)d(from)g(Step)g(2)g(it)g(follo)n(ws)f (that)h Fs(f)1546 1825 y Fo(t)1598 1813 y FA(!)d Fs(f)1745 1825 y Fo(s)1806 1813 y Fx(as)j Fs(t)d FA(!)g Fs(s)j Fx(\(and)g Fs(t)d FA(\025)f Fs(s)p Fx(\))27 b(almost)e(surely)g(with) 365 1913 y(resp)r(ect)k(to)g(b)r(oth)g Fs(\026)1001 1925 y Fo(s)1066 1913 y Fx(and)f Fs(\027)1269 1925 y Fo(s)1305 1913 y Fx(.)41 b(In)29 b(fact,)g(let)g Fs(B)34 b Fx(b)r(e)29 b(either)g(a)f(p)r(ositiv)n(e)h(part)f(in)h(the)h(Hahn)365 2012 y(decomp)r(osition)22 b(of)g Fs(\027)1042 1982 y Fo(s)1037 2033 y(s)1100 2012 y Fx(or)f(an)n(y)h(its)g(measurable)f (subset.)35 b(Then)23 b Fs(f)2425 2024 y Fo(s)2483 2012 y Fx(=)f(1)g(on)g Fs(B)t Fx(.)35 b(Moreo)n(v)n(er,)982 2195 y Fs(\026)1032 2207 y Fo(t)1061 2195 y Fx(\()p Fs(B)t Fx(\))24 b(=)f(\()p Fs(t)18 b FA(\000)g Fs(s)p Fx(\))p Fs(\027)1584 2161 y Fo(s)1579 2215 y(s)1620 2195 y Fx(\()p Fs(B)t Fx(\))i(+)e Fs(o)p Fx(\()p Fs(t)h FA(\000)f Fs(s)p Fx(\))p Fs(;)97 b(t)18 b FA(\000)g Fs(s)23 b FA(!)g Fx(0)p Fs(;)365 2377 y Fx(and)28 b(is)f(p)r(ositiv)n(e)g(and)h(hence)f Fs(f)1350 2389 y Fo(t)1402 2377 y Fx(=)c(1)k(on)h Fs(B)j Fx(for)c Fs(t)h Fx(close)f(enough)g(to)g Fs(s)p Fx(.)490 2477 y Fh(Step)h Fx(4.)p 490 2507 V 27 w(By)f(de\014nition,)846 2663 y Fs(d)p 827 2701 83 4 v 827 2777 a(ds)919 2720 y FA(k)p Fs(\026)1011 2732 y Fo(s)1046 2720 y FA(k)22 b Fx(=)27 b(lim)1198 2769 y Fo(t)p Fn(!)p Fo(s)1344 2663 y FA(k)p Fs(\026)1436 2675 y Fo(t)1465 2663 y FA(k)18 b(\000)g(k)p Fs(\026)1700 2675 y Fo(s)1735 2663 y FA(k)p 1344 2701 433 4 v 1475 2777 a Fs(t)h FA(\000)f Fs(s)1110 2931 y Fx(=)27 b(lim)1198 2980 y Fo(t)p Fn(!)p Fo(s)1335 2818 y Fm(Z)1441 2874 y Fs(f)1482 2886 y Fo(t)1530 2874 y FA(\000)18 b Fs(f)1654 2886 y Fo(s)p 1441 2911 248 4 v 1480 2987 a Fs(t)g FA(\000)g Fs(s)1699 2931 y(\026)1749 2943 y Fo(s)1784 2931 y Fx(\()p Fs(dy)s Fx(\))h(+)j(lim)2037 2980 y Fo(t)p Fn(!)p Fo(s)2174 2818 y Fm(Z)2271 2931 y Fs(f)2312 2943 y Fo(t)2350 2874 y Fs(\026)2400 2886 y Fo(t)2448 2874 y FA(\000)c Fs(\026)2581 2886 y Fo(s)p 2350 2911 267 4 v 2398 2987 a Fs(t)h FA(\000)f Fs(s)2627 2931 y Fx(\()p Fs(dy)s Fx(\))260 b(\(A.2\))365 3156 y(\(if)38 b(b)r(oth)g(limits)f(exist,)i(of)e(course\).)64 b(It)38 b(is)f(easy)f(to)h(see)f(that)i(the)f(second)f(limit)i(here)365 3255 y(alw)n(a)n(ys)26 b(exists)h(and)h(equals)1273 3188 y Fm(R)1343 3255 y Fs(f)1384 3267 y Fo(s)1419 3255 y Fs(\027)1460 3267 y Fo(s)1495 3255 y Fx(\()p Fs(dy)s Fx(\).)38 b(In)27 b(fact,)474 3372 y Fm(Z)571 3485 y Fs(f)612 3497 y Fo(t)651 3429 y Fs(\026)701 3441 y Fo(t)749 3429 y FA(\000)18 b Fs(\026)882 3441 y Fo(s)p 651 3466 V 699 3542 a Fs(t)g FA(\000)g Fs(s)927 3485 y Fx(\()p Fs(dy)s Fx(\))24 b(=)1189 3372 y Fm(Z)1286 3485 y Fs(f)1327 3497 y Fo(s)1372 3429 y Fs(\026)1422 3441 y Fo(t)1470 3429 y FA(\000)18 b Fs(\026)1603 3441 y Fo(s)p 1372 3466 V 1420 3542 a Fs(t)h FA(\000)f Fs(s)1649 3485 y Fx(\()p Fs(dy)s Fx(\))1180 3703 y(+)1263 3590 y Fm(Z)1346 3703 y Fx(\()p Fs(f)1419 3715 y Fo(t)1467 3703 y FA(\000)g Fs(f)1591 3715 y Fo(s)1626 3703 y Fx(\))1658 3610 y Fm(\020)1718 3646 y Fs(\026)1768 3658 y Fo(t)1815 3646 y FA(\000)g Fs(\026)1948 3658 y Fo(s)p 1718 3684 V 1766 3760 a Fs(t)g FA(\000)g Fs(s)2012 3703 y FA(\000)g Fs(\027)2136 3715 y Fo(s)2172 3610 y Fm(\021)2222 3703 y Fx(\()p Fs(dy)s Fx(\))g(+)2474 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(resp)r(ect)g(to)g Fs(\027)2530 4243 y Fo(s)2566 4231 y Fx(.)36 b(Consequen)n(tly)-7 b(,)27 b(to)365 4331 y(complete)h(the)h (pro)r(of)f(it)g(remains)f(to)h(sho)n(w)g(that)g(the)h(\014rst)f(term)g (on)g(the)g(r.h.s.)g(of)g(\(A.2\))365 4430 y(v)-5 b(anishes.)365 4613 y Fg(R)l(emark)30 b Fx(A.2.)41 b(As)30 b(w)n(e)f(sho)n(w)n(ed)f (in)h(Step)h(2,)f(the)g(function)h(\()p Fs(f)2328 4625 y Fo(t)2377 4613 y FA(\000)19 b Fs(f)2502 4625 y Fo(s)2537 4613 y Fx(\))p Fs(=)p Fx(\()p Fs(t)h FA(\000)f Fs(s)p Fx(\))29 b(under)g(the)365 4713 y(in)n(tegral)e(in)i(this)g(term)f (tends)h(to)f(zero)g(almost)g(surely)f(with)i(resp)r(ect)g(to)f Fs(\026)2770 4725 y Fo(s)2805 4713 y Fx(,)h(but)g(unfor-)365 4812 y(tunately)h(this)h(is)e(not)h(enough)g(to)f(conclude)h(that)g (the)h(limit)f(of)g(the)g(in)n(tegral)f(v)-5 b(anishes,)365 4912 y(and)28 b(consequen)n(tly)e(an)i(additional)f(argumen)n(t)f(is)i (required.)490 5095 y Fh(Step)g Fx(5.)p 490 5124 254 4 v 31 w(In)j(order)e(to)i(sho)n(w)f(that)h(the)h(\014rst)e(term)h(in)g (\(A.2\))h(v)-5 b(anishes,)31 b(it)g(is)g(enough)365 5194 y(to)c(sho)n(w)f(that)h(the)g(corresp)r(onding)e(limits)i(of)g (the)g(in)n(tegrals)f(o)n(v)n(er)f(the)i(sets)f Fs(A)2868 5164 y Fl(+)2951 5194 y Fx(and)g Fs(A)3173 5164 y Fn(\000)p eop end %%Page: 134 40 TeXDict begin 134 39 bop 681 725 a Fq(134)2174 b(V.N.)25 b(Kolok)n(oltso)n(v)681 1016 y Fx(v)-5 b(anish,)27 b(where)f Fs(Y)42 b Fx(=)23 b Fs(A)1439 986 y Fl(+)1511 1016 y FA([)17 b Fs(A)1645 986 y Fn(\000)1719 1016 y FA([)g Fs(A)1853 986 y Fl(0)1918 1016 y Fx(is)27 b(the)g(Hahn)g(decomp)r (osition)f(of)h Fs(Y)46 b Fx(with)27 b(resp)r(ect)681 1116 y(to)21 b(the)h(measure)f Fs(\026)1281 1128 y Fo(s)1316 1116 y Fx(.)35 b(Let)22 b(us)g(consider)e(only)h Fs(A)2173 1085 y Fl(+)2250 1116 y Fx(\()p Fs(A)2344 1085 y Fn(\000)2423 1116 y Fx(is)g(considered)g(similarly\).)34 b(Hence,)681 1215 y(as)27 b Fs(f)824 1227 y Fo(s)882 1215 y Fx(=)c(1)k(on)g Fs(A)1216 1185 y Fl(+)1299 1215 y Fx(almost)g(surely)-7 b(,)27 b(w)n(e)g(need)h(to)f(sho)n(w)g(that)1689 1436 y(lim)1685 1486 y Fo(t)p Fn(!)p Fo(s)1822 1323 y Fm(Z)1820 1562 y Fo(A)1929 1380 y Fs(f)1970 1392 y Fo(t)2017 1380 y FA(\000)18 b Fx(1)p 1929 1417 213 4 v 1950 1493 a Fs(t)g FA(\000)g Fs(s)2151 1436 y(\026)2201 1448 y Fo(s)2237 1436 y Fx(\()p Fs(dy)s Fx(\))23 b(=)g(0)813 b(\(A.3\))681 1723 y(where)34 b Fs(A)i Fx(is)e(a)h(measurable)f(subset)g(of)h Fs(Y)54 b Fx(suc)n(h)35 b(that)g(\()p Fs(\026)2564 1735 y Fo(s)2600 1723 y Fx(\))p FA(j)2655 1735 y Fo(A)2744 1723 y Fx(is)g(a)g(p)r(ositiv)n(e)f(measure.)681 1823 y(Using)k(no)n(w)g(the)h(Leb)r(esgue)f(decomp)r(osition)g(of)g(\()p Fs(\027)2369 1835 y Fo(s)2405 1823 y Fx(\))p FA(j)2460 1835 y Fo(A)2553 1823 y Fx(in)n(to)g(the)h(sum)g(of)f(a)g(singular)681 1923 y(and)27 b(absolutely)g(con)n(tin)n(uous)f(parts)h(with)h(resp)r (ect)f(to)g Fs(\026)2489 1935 y Fo(s)2524 1923 y Fx(,)h(w)n(e)f(can)g (and)g(will)h(reduce)f(the)681 2022 y(discussion)c(to)h(the)h(case)e (when)h Fs(\027)1730 2034 y Fo(s)1790 2022 y Fx(is)g(absolutely)f(con)n (tin)n(uous)h(with)g(resp)r(ect)g(to)g Fs(\026)3288 2034 y Fo(s)3348 2022 y Fx(on)g Fs(A)p Fx(.)805 2122 y(In)n(tro)r(ducing)e (the)h(set)g Fs(A)1575 2134 y Fo(t)1627 2122 y Fx(=)g FA(f)p Fs(y)i FA(2)e Fs(A)h Fx(:)f Fs(f)2074 2134 y Fo(t)2103 2122 y Fx(\()p Fs(y)s Fx(\))g FA(\024)g Fx(0)p FA(g)e Fx(one)h(can)h(clearly)e(replace)g Fs(A)i Fx(b)n(y)g Fs(A)3516 2134 y Fo(t)681 2222 y Fx(in)i(\(A.3\).)36 b(Consequen)n(tly)-7 b(,)25 b(to)g(get)g(\(A.3\))g(it)g(is)g(enough)f (to)h(sho)n(w)f(that)h Fs(\026)2978 2234 y Fo(s)3014 2222 y Fx(\()p Fs(A)3108 2234 y Fo(t)3138 2222 y Fx(\))e(=)g Fs(o)p Fx(\()p Fs(t)13 b FA(\000)g Fs(s)p Fx(\))681 2321 y(as)27 b Fs(t)c FA(!)g Fs(s)p Fx(.)37 b(This)27 b(will)h(b)r(e)g(done) f(in)h(the)g(next)g(\014nal)g(step.)805 2421 y Fh(Step)g Fx(6.)p 805 2450 254 4 v 30 w(F)-7 b(rom)29 b(the)g(de\014nition)h(of)g Fs(A)1983 2433 y Fo(t)2042 2421 y Fx(it)g(follo)n(ws)e(that)i Fs(\026)2633 2433 y Fo(t)2662 2421 y Fx(\()p Fs(B)t Fx(\))d FA(\024)f Fx(0)j(for)g(an)n(y)f Fs(B)j FA(\032)26 b Fs(A)3516 2433 y Fo(t)681 2520 y Fx(and)h(hence)1456 2620 y Fs(\026)1506 2632 y Fo(s)1542 2620 y Fx(\()p Fs(B)t Fx(\))19 b(+)f(\()p Fs(t)g FA(\000)g Fs(s)p Fx(\))p Fs(\027)2050 2632 y Fo(s)2086 2620 y Fx(\()p Fs(B)t Fx(\))h(+)f Fs(o)p Fx(\()p Fs(t)h FA(\000)f Fs(s)p Fx(\))24 b FA(\024)e Fx(0)p Fs(;)584 b Fx(\(A.4\))681 2769 y(where)23 b Fs(o)p Fx(\()p Fs(t)11 b FA(\000)g Fs(s)p Fx(\))24 b(is)g(uniform,)g(i.e.)g FA(k)p Fs(o)p Fx(\()p Fs(t)11 b FA(\000)g Fs(s)p Fx(\))p FA(k)p Fs(=)p Fx(\()p Fs(t)g FA(\000)g Fs(s)p Fx(\))22 b FA(!)h Fx(0)g(as)g Fs(t)g FA(!)h Fs(s)p Fx(.)35 b(Notice)24 b(\014rst)g(that)g(if)681 2869 y Fs(A)743 2881 y Fo(t)795 2869 y Fx(=)f Fs(B)950 2834 y Fl(+)946 2890 y Fo(t)1024 2869 y FA([)c Fs(B)1165 2834 y Fn(\000)1161 2890 y Fo(t)1239 2869 y FA([)g Fs(B)1380 2839 y Fl(0)1376 2890 y Fo(t)1445 2869 y Fx(is)28 b(the)g(Hahn)g(decomp)r(osition)f(of)g Fs(A)2599 2881 y Fo(t)2657 2869 y Fx(on)g(the)h(p)r(ositiv)n(e,)f (negativ)n(e)681 2969 y(and)k(zero)g(parts)g(of)h(the)h(measure)d Fs(\027)1858 2981 y Fo(s)1894 2969 y Fx(,)j(then)f Fs(\026)2193 2981 y Fo(s)2229 2969 y Fx(\()p Fs(B)2328 2933 y Fl(+)2324 2989 y Fo(t)2405 2969 y FA([)21 b Fs(B)2548 2939 y Fl(0)2544 2989 y Fo(t)2586 2969 y Fx(\))30 b(=)g Fs(o)p Fx(\()p Fs(t)22 b FA(\000)f Fs(s)p Fx(\))32 b(uniformly)f(\(as)681 3068 y(it)36 b(follo)n(ws)g(directly)g(from)g(\(A.4\)\),)j(and)d (consequen)n(tly)g(w)n(e)g(can)f(and)i(will)f(reduce)g(our)681 3168 y(discussion)30 b(to)h(the)h(case)e(when)h Fs(\027)1765 3180 y Fo(s)1832 3168 y Fx(is)g(a)g(negativ)n(e)f(measure)g(on)h Fs(A)p Fx(.)48 b(In)31 b(this)g(case)g(\(A.4\))681 3268 y(implies)d(that)1450 3367 y Fs(\026)1500 3379 y Fo(s)1536 3367 y Fx(\()p Fs(A)1630 3379 y Fo(t)1659 3367 y Fx(\))c FA(\024)e Fx(\()p Fs(t)d FA(\000)f Fs(s)p Fx(\)\()p FA(\000)p Fs(\027)2175 3379 y Fo(s)2211 3367 y Fx(\)\()p Fs(A)2337 3379 y Fo(t)2367 3367 y Fx(\))g(+)h Fs(o)p Fx(\()p Fs(t)f FA(\000)g Fs(s)p Fx(\))681 3517 y(and)29 b(it)h(remains)e(to)h(sho)n(w) g(that)g Fs(\027)1773 3529 y Fo(s)1809 3517 y Fx(\()p Fs(A)1903 3529 y Fo(t)1932 3517 y Fx(\))e(=)e Fs(o)p Fx(\(1\))2227 3529 y Fo(t)p Fn(!)p Fo(s)2354 3517 y Fx(.)42 b(T)-7 b(o)29 b(see)g(this)h(w)n(e)e(observ)n(e)g(that)i(for)681 3616 y(an)n(y)d Fs(s)p Fx(,)g Fs(Y)47 b Fx(has)27 b(the)h(represen)n (tation)d Fs(Y)42 b Fx(=)23 b FA([)2088 3586 y Fn(1)2088 3637 y Fo(n)p Fl(=0)2217 3616 y Fs(Y)2265 3628 y Fo(n)2311 3616 y Fx(,)28 b(where)f FA(j)p Fs(\026)2675 3628 y Fo(s)2710 3616 y FA(j)p Fx(\()p Fs(Y)2813 3628 y Fl(0)2851 3616 y Fx(\))c(=)g(0)k(and)1354 3799 y Fs(Y)1402 3811 y Fo(n)1470 3799 y Fx(=)c FA(f)p Fs(y)i FA(2)f Fs(Y)41 b Fx(:)23 b Fs(f)1921 3811 y Fo(t)1973 3799 y Fx(=)g Fs(f)2102 3811 y Fo(s)2220 3799 y Fx(for)k FA(j)p Fs(t)19 b FA(\000)f Fs(s)p FA(j)23 b(\024)f Fx(1)p Fs(=n)p FA(g)p Fs(:)681 3982 y Fx(Clearly)i Fs(Y)1015 3994 y Fo(n)1084 3982 y FA(\032)e Fs(Y)1219 3994 y Fo(n)p Fl(+1)1374 3982 y Fx(for)j(an)n(y)g Fs(n)e FA(6)p Fx(=)f(0)k(and)f Fs(A)2103 3994 y Fo(t)2155 3982 y FA(\032)e Fs(Y)33 b FA(n)14 b Fs(Y)2428 3994 y Fo(n)2499 3982 y Fx(whenev)n(er)24 b Fs(t)14 b FA(\000)g Fs(s)23 b FA(\024)g Fx(1)p Fs(=n)p Fx(.)35 b(Hence)681 4081 y Fs(A)743 4093 y Fo(t)799 4081 y Fx(are)26 b(subsets)g(of)h(a)f (decreasing)g(family)g(of)h(sets)g(with)g(an)f(in)n(tersection)g(of)h Fs(\026)3186 4093 y Fo(s)3221 4081 y Fx(-measure)681 4181 y(zero.)50 b(As)32 b Fs(\027)1071 4193 y Fo(s)1139 4181 y Fx(is)g(absolutely)g(con)n(tin)n(uous)f(with)i(resp)r(ect)f(to)g Fs(\026)2686 4193 y Fo(s)2754 4181 y Fx(the)h(same)f(holds)g(for)g Fs(\027)3510 4193 y Fo(s)681 4280 y Fx(and)27 b(hence)h Fs(\027)1114 4292 y Fo(s)1149 4280 y Fx(\()p Fs(A)1243 4292 y Fo(t)1273 4280 y Fx(\))23 b(=)g Fs(o)p Fx(\(1\))1562 4292 y Fo(t)p Fn(!)p Fo(s)1689 4280 y Fx(,)28 b(whic)n(h)f(completes)h (the)g(pro)r(of)f(of)g(the)h(lemma.)262 b Ff(2)681 4463 y Fg(R)l(emark)30 b Fx(A.3.)41 b(Supp)r(ose)35 b(the)g(assumptions)f (of)g(Lemma)h(A)g(hold)f(and)h Fs(L)p Fx(\()p Fs(y)s Fx(\))f(is)h(a)f(mea-)681 4563 y(surable,)24 b(non-negativ)n(e)g(and)h (ev)n(erywhere)e(\014nite)i(function)h(on)f Fs(Y)43 b Fx(suc)n(h)25 b(that)g FA(k)p Fs(L\026)3310 4575 y Fo(s)3345 4563 y FA(k)f Fx(and)681 4662 y FA(k)p Fs(L\027)821 4674 y Fo(s)855 4662 y FA(k)i Fx(are)g(uniformly)h(b)r(ounded)g(for)f Fs(s)d FA(2)g Fx([0)p Fs(;)14 b(t)p Fx(].)36 b(Then)27 b(\(A.1\))g(holds)f(with)h Fs(L\026)3202 4674 y Fo(t)3258 4662 y Fx(and)f Fs(L\027)3516 4674 y Fo(t)681 4762 y Fx(instead)d(of)h Fs(\026)1104 4774 y Fo(t)1157 4762 y Fx(and)f Fs(\027)1355 4774 y Fo(t)1408 4762 y Fx(resp)r(ectiv)n(ely) -7 b(.)35 b(In)24 b(fact,)g(though)g Fs(s)f FA(7!)g Fs(L\027)2712 4774 y Fo(s)2770 4762 y Fx(ma)n(y)g(b)r(e)h(discon)n(tin)n(uous)681 4862 y(in)34 b(the)g(sense)f(of)h(norm,)g(one)g(can)f(write)g(the)i (required)d(iden)n(tit)n(y)i(\014rst)g(with)g(the)g(space)681 4961 y Fs(Y)729 4973 y Fo(m)825 4961 y Fx(instead)f(of)g Fs(Y)19 b Fx(,)34 b(where)f Fs(Y)1635 4973 y Fo(m)1730 4961 y Fx(=)e FA(f)p Fs(y)k Fx(:)d Fs(L)p Fx(\()p Fs(y)s Fx(\))g FA(\024)f Fs(m)p FA(g)p Fx(,)j(and)f(then)h(pass)e(to)h(the)g (limit)h(as)681 5061 y Fs(m)23 b FA(!)g(1)p Fx(.)p eop end %%Page: 135 41 TeXDict begin 135 40 bop 365 725 a Fq(Kinetic)26 b(equations)g(for)g (jump-t)n(yp)r(e)f(in)n(teractions)1257 b(135)365 1016 y FB(Lemma)32 b(A.2.)40 b Fh(Supp)r(ose)22 b Fs(X)28 b Fh(is)21 b(a)g(lo)r(cally)g(compact)g(metric)g(space,)h Fs(L)f Fh(is)g(a)g(non-negativ)n(e)365 1116 y(con)n(tin)n(uous)i (function)i(on)f(it)g(and)g Fs(a)p Fh(,)h Fs(b)f Fh(are)f(t)n(w)n(o)g (p)r(ositiv)n(e)h(constan)n(ts.)34 b(Then)25 b(the)f(solution)365 1215 y(to)k(the)g(measure-v)-5 b(alued)26 b(ordinary)g(di\013eren)n (tial)h(equation)998 1429 y Fx(_)-39 b Fs(\026)p Fx(\()p Fs(dx)p Fx(\))24 b(=)f FA(\000)p Fs(aL)p Fx(\()p Fs(x)p Fx(\))p Fs(\026)p Fx(\()p Fs(dx)p Fx(\))c FA(\000)f Fs(b)1941 1304 y Fm(R)2010 1371 y Fs(L)p Fx(\()p Fs(u)p Fx(\))p Fs(\026)p Fx(\()p Fs(du)p Fx(\))p 1941 1409 444 4 v 2025 1419 a Fm(R)2094 1486 y Fs(\026)p Fx(\()p Fs(du)p Fx(\))2408 1429 y Fs(\026)p Fx(\()p Fs(dx)p Fx(\))426 b(\(A.5\))365 1647 y Fh(on)28 b Fx(\()p Fh(p)r(ositiv)n(e)5 b Fx(\))27 b Fh(measures)f Fs(\026)i Fh(on)f(a)h Fs(X)33 b Fh(with)c(initial)e (condition)h Fs(\026)2422 1659 y Fl(0)2487 1647 y Fh(equals)439 1914 y Fs(\026)489 1926 y Fo(t)518 1914 y Fx(\()p Fs(dx)p Fx(\))d(=)d(exp)p FA(f\000)p Fs(atL)p Fx(\()p Fs(x)p Fx(\))p FA(g)p Fs(\026)1352 1926 y Fl(0)1388 1914 y Fx(\()p Fs(dx)p Fx(\))14 b(exp)1684 1796 y Fm(\032)1747 1914 y FA(\000)p Fs(b)1908 1784 y Fo(t)1861 1801 y Fm(Z)1867 2036 y Fl(0)1967 1789 y Fm(R)2037 1856 y Fs(L)p Fx(\()p Fs(u)p Fx(\))g(exp)o FA(f\000)p Fs(asL)p Fx(\()p Fs(u)p Fx(\))p FA(g)p Fs(\026)2797 1868 y Fl(0)2832 1856 y Fx(\()p Fs(du)p Fx(\))p 1967 1894 1021 4 v 2059 1904 a Fm(R)2128 1971 y Fx(exp)p FA(f\000)p Fs(asL)p Fx(\()p Fs(u)p Fx(\))p FA(g)p Fs(\026)2706 1983 y Fl(0)2741 1971 y Fx(\()p Fs(du)p Fx(\))3011 1914 y Fs(ds)3093 1796 y 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Fa(1541)p Fq(,)842 3966 y(1{260.)681 4088 y([12])43 b Fr(P.B.)35 b(Dubo)n(vski)e Fq(\(1999\))56 b(A)32 b(\\triangle")j(of)e (in)n(terconnected)f(coagulation)i(mo)r(dels.)56 b Fb(J.)842 4179 y(Phys.)28 b(A:)f(Math.)g(Gen.)f Fa(32)p Fq(,)g(781{793.)681 4302 y([13])43 b Fr(P.B.)37 b(Dubo)n(vski)r(i)h(and)f(I.W.)g(Stew)-7 b(ar)i(t)35 b Fq(\(1996\))63 b(Existence,)37 b(uniqueness)e(and)f(mass) 842 4393 y(conserv)l(ation)i(for)h(the)e(coagulation-fragmen)n(tation)k (equation.)65 b Fb(Math.)37 b(Metho)l(d)h(Appl.)842 4484 y(Sci.)25 b Fa(19)p Fq(,)h(571{591.)681 4607 y([14])43 b Fr(E.)22 b(D)n(ynkin)c Fq(\(1994\))25 b Fb(A)n(n)c(Intr)l(o)l (duction)j(to)e(Br)l(anching)g(Me)l(asur)l(e-V)-6 b(alue)l(d)25 b(Pr)l(o)l(c)l(esses)p Fq(.)d(CRM)842 4698 y(monograph)k(series)h Fa(6)p Fq(,)f(AMS,)g(Pro)n(vidence)f(RI.)681 4821 y([15])43 b Fr(S.N.)30 b(Ethier)g(and)g(T.G.)g(Kur)-5 b(tz)27 b Fq(\(1986\))43 b Fb(Markov)30 b(Pr)l(o)l(c)l(esses.)i(Char)l (acterization)h(and)842 4912 y(Conver)l(genc)l(e)p Fq(.)28 b(John)e(Wiley)g(&)f(Sons.)681 5034 y([16])43 b Fr(M.Z.)29 b(Guo,)h(G.Z.)g(P)-7 b(ap)i(anicola)n(u)30 b(and)f(S.R.S.)g(V)-9 b(aradhan)26 b Fq(\(1988\))40 b(Nonlinear)28 b(di\013u-)842 5126 y(sion)23 b(limit)g(for)g(a)f(system)h(with)f(nearest)h(neigh)n(b) r(or)g(in)n(teractions.)29 b Fb(Commun.)24 b(Math.)h(Phys.)842 5217 y Fa(118)p Fq(,)h(31{59.)p eop end %%Page: 137 43 TeXDict begin 137 42 bop 365 725 a Fq(Kinetic)26 b(equations)g(for)g (jump-t)n(yp)r(e)f(in)n(teractions)1257 b(137)365 1016 y([17])43 b Fr(J.)e(Hofba)n(uer)f(and)g(K.)g(Sigmund)35 b Fq(\(1998\))70 b Fb(Evolutionary)40 b(Games)f(and)g(Population)526 1107 y(Dynamics)p Fq(.)c(Cam)n(bridge)27 b(Univ)n(ersit)n(y)d(Press.) 365 1231 y([18])43 b Fr(I.)22 b(Jeon)d Fq(\(1998\))25 b(Existence)19 b(of)h(Gelling)h(Solutions)e(for)h(coagulation-fragmen)n (tation)i(equa-)526 1322 y(tions.)35 b Fb(Commun.)27 b(Math.)h(Phys.)e Fa(194)p Fq(,)g(541{567.)365 1446 y([19])43 b Fr(V.)34 b(K)n(olok)n(ol)-5 b(tso)n(v)35 b 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