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1、ThispageintentionallyleftblankFunctionalAnalysisforProbabilityandStochasticProcesses.AnIntroductionThistextisdesignedbothforstudentsofprobabilityandstochasticprocessesandforstudentsoffunctionalanalysis.Forthereadernotfamiliarwithfunctionalanalysisadetailedintroductio
2、ntonecessarynotionsandfactsisprovided.However,thisisnotastraighttextbookinfunctionalanalysis;rather,itpresentssomechosenpartsoffunctionalanalysisthathelpunderstandideasfromprobabilityandstochasticprocesses.ThesubjectsrangefrombasicHilbertandBanachspaces,throughweakto
3、pologiesandBanachalgebras,tothetheoryofsemigroupsofboundedlinearoperators.Numerousstandardandnon-standardexamplesandexercisesmakethebooksuitableforbothatextbookforacourseandforself-study.adambobrowskiisaProfessorofMathematicsatLublinUniversityofTechnology.FunctionalA
4、nalysisforProbabilityandStochasticProcessesAnIntroductionA.BOBROWSKIcambridgeuniversitypressCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,S?oPauloCambridgeUniversityPressTheEdinburghBuilding,Cambridgecb22ru,UKPublishedintheUnitedStatesofAmericabyCambridgeUniv
5、ersityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521831666?CambridgeUniversityPress2005Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplace
6、withoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintformat2005isbn-13978-0-511-13039-7eBook(NetLibrary)isbn-100-511-13039-2eBook(NetLibrary)isbn-13978-0-521-83166-6hardbackisbn-100-521-83166-0hardbackisbn-13978-0-521-53937-1paperbackisbn-100-52
7、1-53937-4paperbackCambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofurlsforexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.Tothemostenthusiasti
8、cwriterever–mysonRadek.ContentsPrefacepagexi1Preliminaries,notationsandconventions11.1Elementsoftopology11.2Measuretheory31.3Functi
