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1、FoundationsofModernProbabilityOlavKallenbergSpringerPrefaceSomethirtyyearsagoitwasstillpossible,asLo`evesoablydemonstrated,towriteasinglebookinprobabilitytheorycontainingpracticallyeverythingworthknowinginthesubject.Thesubsequentdevelopmenthasbeenex-plosive,andtodayac
2、orrespondingcomprehensivecoveragewouldrequireawholelibrary.Researchersandgraduatestudentsalikeseemcompelledtoaratherextremedegreeofspecialization.Asaresult,thesubjectisthreatenedbydisintegrationintodozensorhundredsofsubfields.Atthesametimetheinteractionbetweentheareasi
3、slivelierthanever,andthereisasteadilygrowingcoreofkeyresultsandtechniquesthateveryprobabilistneedstoknow,ifonlytoreadtheliteratureinhisorherownfield.Thus,itseemsessentialthatweallhaveatleastageneraloverviewofthewholearea,andweshoulddowhatwecantokeepthesubjecttogether.T
4、hepresentvolumeisanearnestattemptinthatdirection.Myoriginalaimwastowriteabookabout“everything.”Variousspaceandtimeconstraintsforcedmetoacceptmoremodestandrealisticgoalsfortheproject.Thus,“foundations”hadtobeunderstoodinthenarrowersenseoftheearly1970s,andtherewasnoroom
5、forsomeofthemorerecentdevelopments.Iespeciallyregrettheomissionoftopicssuchaslargede-viations,GibbsandPalmmeasures,interactingparticlesystems,stochasticdifferentialgeometry,Malliavincalculus,SPDEs,measure-valueddiffusions,andbranchingandsuperprocesses.Clearlyplentyoffun
6、damentalandin-triguingmaterialremainsforapossiblesecondvolume.Evenwithmymorelimited,revisedambitions,Ihadtobeextremelyselectiveinthechoiceofmaterial.Moreimportantly,itwasnecessarytolookforthemosteconomicalapproachtoeveryresultIdiddecidetoinclude.Inthelatterrespect,Iwa
7、ssurprisedtoseehowmuchcouldactuallybedonetosimplifyandstreamlineproofs,oftenhandeddownthroughgenerationsoftextbookwriters.Mygeneralpreferencehasbeenforresultsconveyingsomenewideaorrelationship,whereasmanypropositionsofamoretechnicalnaturehavebeenomitted.Inthesamevein,
8、Ihaveavoidedtechnicalorcomputationalproofsthatgivelittleinsightintotheprovenresults.Thisconformswithmyconvictionthatthelogic
