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1、UniformzJ'.LThebookshowshowthecentrallimittheoremforindependent,identicallydistributedrandomvariableswithvaluesingeneral,multidimensionalspacesholdsuniformlyoversomelargeclassesoffunctions.Thebookcontains,withcompleteproofs,theFernique-Talagrandmajoriz-ingmea
2、suretheoremforGaussianprocesses,anextendedtreatmentofVapnik-Cernovenkiscombinatorics,theOssianderL2bracketingcentrallimittheorem,theGine-Zinnbootstrapcentrallimittheoreminprobability,theBronsteintheoremonapproximationofconvexsets,andtheShortheoremonratesofcon
3、vergenceoverlowerlayers.Thebookincorporatesanupdatedformoftheauthor's1984St.-Flourlecturenotesandalsogivesvariousresultsoftheauthor'snotpreviouslycollectedinoneplace.AnumberofrecentresultsofTalagrandandothersaresurveyedwithoutproofsinseparatesections.Thebookw
4、illinterestmathematiciansworkinginprobability,mathematicalstatisticians,andcomputerscientistsworkingincomputerlearningtheory.R.M.DudleyisProfessorofMathematicsattheMassachusettsInstituteofTechnologyinCambridge,Massachusetts.CambridgeStudiesinAdvancedMathemati
5、cs63EditorialBoard:W.Fulton,D.J.H.Garling,T.tomDieck,P.WaltersAlreadypublished2K.PetersenErgodictheory3P.T.JohnstoneStonespaces5J.-P.KahaneSomerandomseriesoffunctions,2ndedition7J.Lambek&P.J.ScottIntroductiontohigher-ordercategoricallogic8H.MatsumuraCommutati
6、veringtheory9C.B.ThomasCharacteristicclassesandthecohomologyoffinitegroups10M.AschbacherFinitegrouptheory11J.L.AlperinLocalrepresentationtheory12P.KoosisThelogarithmicintegralI13A.PietschEigenvaluesands-numbers14S.J.PattersonAnintroductiontothetheoryoftheRiem
7、annzeta-function15H.J.BauesAlgebraichomotopy16V.S.VaradarajanIntroductiontoharmonicanalysisonsemisimpleLiegroups17W.Dicks&M.DunwoodyGroupsactingongraphs18L.J.Corwin&F.P.GreenleafRepresentationsofnilpotentLiegroupsandtheirapplications19R.Fritsch&R.PiccininiCel
8、lularstructuresintopology20H.KlingenIntroductorylecturesonSiegelmodularforms21P.KoosisThelogarithmicintegralII22M.J.CollinsRepresentationsandcharactersoffinitegroups24H.KunitaStochasticfl
