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1、PrefaceSomethirtyyearsagoitwasstillpossible,asLo`evesoablydemonstrated,towriteasinglebookinprobabilitytheorycontainingpracticallyeverythingworthknowinginthesubject.Thesubsequentdevelopmenthasbeenex-plosive,andtodayacorrespondingcomprehensivecoveragewouldrequireawholelibrary.Researchersandgraduates
2、tudentsalikeseemcompelledtoaratherextremedegreeofspecialization.Asaresult,thesubjectisthreatenedbydisintegrationintodozensorhundredsofsubfields.Atthesametimetheinteractionbetweentheareasislivelierthanever,andthereisasteadilygrowingcoreofkeyresultsandtechniquesthateveryprobabilistneedstoknow,ifonlyt
3、oreadtheliteratureinhisorherownfield.Thus,itseemsessentialthatweallhaveatleastageneraloverviewofthewholearea,andweshoulddowhatwecantokeepthesubjecttogether.Thepresentvolumeisanearnestattemptinthatdirection.Myoriginalaimwastowriteabookabout“everything.”Variousspaceandtimeconstraintsforcedmetoacceptm
4、oremodestandrealisticgoalsfortheproject.Thus,“foundations”hadtobeunderstoodinthenarrowersenseoftheearly1970s,andtherewasnoroomforsomeofthemorerecentdevelopments.Iespeciallyregrettheomissionoftopicssuchaslargede-viations,GibbsandPalmmeasures,interactingparticlesystems,stochasticdifferentialgeometry,
5、Malliavincalculus,SPDEs,measure-valueddiffusions,andbranchingandsuperprocesses.Clearlyplentyoffundamentalandin-triguingmaterialremainsforapossiblesecondvolume.Evenwithmymorelimited,revisedambitions,Ihadtobeextremelyselectiveinthechoiceofmaterial.Moreimportantly,itwasnecessarytolookforthemosteconomi
6、calapproachtoeveryresultIdiddecidetoinclude.Inthelatterrespect,Iwassurprisedtoseehowmuchcouldactuallybedonetosimplifyandstreamlineproofs,oftenhandeddownthroughgenerationsoftextbookwriters.Mygeneralpreferencehasbeenforresultsconveyingsomenewideaorrelationship,whereasmanypropositionsofamoretechnical
7、naturehavebeenomitted.Inthesamevein,Ihaveavoidedtechnicalorcomputationalproofsthatgivelittleinsightintotheprovenresults.Thisconformswithmyconvictionthatthelogicalstructureiswhatmattersmostinmathematics,evenwhenap
