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1、PrefaceSomethirtyyearsagoitwasstillpossible,asLo`evesoablydemonstrated,towriteasinglebookinprobabilitytheorycontainingpracticallyeverythingworthknowinginthesubject.Thesubsequentdevelopmenthasbeenex-plosive,andtodayacorrespondingcomprehensivecoveragewouldrequireawholelibrary.Researche
2、rsandgraduatestudentsalikeseemcompelledtoaratherextremedegreeofspecialization.Asaresult,thesubjectisthreatenedbydisintegrationintodozensorhundredsofsub?elds.Atthesametimetheinteractionbetweentheareasislivelierthanever,andthereisasteadilygrowingcoreofkeyresultsandtechniquesthateverypr
3、obabilistneedstoknow,ifonlytoreadtheliteratureinhisorherown?eld.Thus,itseemsessentialthatweallhaveatleastageneraloverviewofthewholearea,andweshoulddowhatwecantokeepthesubjecttogether.Thepresentvolumeisanearnestattemptinthatdirection.Myoriginalaimwastowriteabookabout“everything.”Vario
4、usspaceandtimeconstraintsforcedmetoacceptmoremodestandrealisticgoalsfortheproject.Thus,“foundations”hadtobeunderstoodinthenarrowersenseoftheearly1970s,andtherewasnoroomforsomeofthemorerecentdevelopments.Iespeciallyregrettheomissionoftopicssuchaslargede-viations,GibbsandPalmmeasures,i
5、nteractingparticlesystems,stochasticdi?erentialgeometry,Malliavincalculus,SPDEs,measure-valueddi?usions,andbranchingandsuperprocesses.Clearlyplentyoffundamentalandin-triguingmaterialremainsforapossiblesecondvolume.Evenwithmymorelimited,revisedambitions,Ihadtobeextremelyselectiveinthe
6、choiceofmaterial.Moreimportantly,itwasnecessarytolookforthemosteconomicalapproachtoeveryresultIdiddecidetoinclude.Inthelatterrespect,Iwassurprisedtoseehowmuchcouldactuallybedonetosimplifyandstreamlineproofs,oftenhandeddownthroughgenerationsoftextbookwriters.Mygeneralpreferencehasbeen
7、forresultsconveyingsomenewideaorrelationship,whereasmanypropositionsofamoretechnicalnaturehavebeenomitted.Inthesamevein,Ihaveavoidedtechnicalorcomputationalproofsthatgivelittleinsightintotheprovenresults.Thisconformswithmyconvictionthatthelogicalstructureiswhatmattersmostinmathematic
8、s,evenwhenap
