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1、GiuseppeDaPratoAnIntroductiontoInfinite-DimensionalAnalysis123GiuseppeDaPratoScuolaNormaleSuperiorePiazzadeiCavalieri756100Pisa,Italye-mail:daprato@sns.itMathematicsSubjectClassification(2000):37L55,60H10,46T12,60J65,60J25LibraryofCongressControlNumber:20069
2、24566ISBN-103-540-29020-6SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-29020-9SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse
3、ofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Dupli-cationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusem
4、ustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.com©Springer-VerlagBerlinHeidelberg2006PrintedinGermanyTheuseofgeneraldescriptivenames,registerednames,tradema
5、rks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:ErichKirchner,HeidelbergTypesettingbytheauthorandSPIPublisherServicesusingaS
6、pringerLATEXmacropackagePrintedonacid-freepaper1150058241/sz-543210PrefaceThisvolumeisarevisedandextendedversionofthelecturenotesconcerningaone-yearcourseoninfinitedimensionalanalysisdeliveredatScuolaNormaleSuperioreinrecentyears,see[6].Thelecturesweredesign
7、edforanaudiencehavingbasicknowledgeoffunctionalanalysisandmeasuretheorybutnotfamiliarwithprobabilitytheory.Themainaimwastogiveanintroductiontotheanalysisinasep-arableHilbertspaceHofinfinitedimensions.ItiswellknownthatthereisnonaturalanalogueoftheLebesguemeas
8、ureonaninfinitedi-mensionalHilbertspace.AnaturalsubstituteisprovidedbyGaussianmeasureswhichareintroducedinChapter1.Theyarefirstdefinedonafinitedimensionalspaceandthen,throughaninfiniteproductofmeasures,onth
