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1、FoundationsofModernProbabilityOlavKallenbergSpringerPrefaceSomethirtyyearsagoitwasstillpossible,asLo`evesoablydemonstrated,towriteasinglebookinprobabilitytheorycontainingpracticallyeverythingworthknowinginthesubject.Thesubsequentdevelopmenthasbeenex-plosive,
2、andtodayacorrespondingcomprehensivecoveragewouldrequireawholelibrary.Researchersandgraduatestudentsalikeseemcompelledtoaratherextremedegreeofspecialization.Asaresult,thesubjectisthreatenedbydisintegrationintodozensorhundredsofsubfields.Atthesametimetheinterac
3、tionbetweentheareasislivelierthanever,andthereisasteadilygrowingcoreofkeyresultsandtechniquesthateveryprobabilistneedstoknow,ifonlytoreadtheliteratureinhisorherownfield.Thus,itseemsessentialthatweallhaveatleastageneraloverviewofthewholearea,andweshoulddowhatw
4、ecantokeepthesubjecttogether.Thepresentvolumeisanearnestattemptinthatdirection.Myoriginalaimwastowriteabookabout“everything.”Variousspaceandtimeconstraintsforcedmetoacceptmoremodestandrealisticgoalsfortheproject.Thus,“foundations”hadtobeunderstoodinthenarrow
5、ersenseoftheearly1970s,andtherewasnoroomforsomeofthemorerecentdevelopments.Iespeciallyregrettheomissionoftopicssuchaslargede-viations,GibbsandPalmmeasures,interactingparticlesystems,stochasticdifferentialgeometry,Malliavincalculus,SPDEs,measure-valueddiffusion
6、s,andbranchingandsuperprocesses.Clearlyplentyoffundamentalandin-triguingmaterialremainsforapossiblesecondvolume.Evenwithmymorelimited,revisedambitions,Ihadtobeextremelyselectiveinthechoiceofmaterial.Moreimportantly,itwasnecessarytolookforthemosteconomicalapp
7、roachtoeveryresultIdiddecidetoinclude.Inthelatterrespect,Iwassurprisedtoseehowmuchcouldactuallybedonetosimplifyandstreamlineproofs,oftenhandeddownthroughgenerationsoftextbookwriters.Mygeneralpreferencehasbeenforresultsconveyingsomenewideaorrelationship,where
8、asmanypropositionsofamoretechnicalnaturehavebeenomitted.Inthesamevein,Ihaveavoidedtechnicalorcomputationalproofsthatgivelittleinsightintotheprovenresults.Thisconformswithmyconvictionthatthelogic
