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1、FunctionalAnalysisforProbabilityandStochasticProcesses.AnIntroductionThistextisdesignedbothforstudentsofprobabilityandstochasticprocessesandforstudentsoffunctionalanalysis.Forthereadernotfamiliarwithfunctionalanalysisadetailedintroductiontonecessarynotionsandfactsisprovided.However,
2、thisisnotastraighttextbookinfunctionalanalysis;rather,itpresentssomechosenpartsoffunctionalanalysisthathelpunderstandideasfromprobabilityandstochasticprocesses.ThesubjectsrangefrombasicHilbertandBanachspaces,throughweaktopologiesandBanachalgebras,tothetheoryofsemigroupsofboundedline
3、aroperators.Numerousstandardandnon-standardexamplesandexercisesmakethebooksuitableforbothatextbookforacourseandforself-study.adambobrowskiisaProfessorofMathematicsatLublinUniversityofTechnology.FunctionalAnalysisforProbabilityandStochasticProcessesAnIntroductionA.BOBROWSKIcambridgeu
4、niversitypressCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,Cambridgecb22ru,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521831666©Cam
5、bridgeUniversityPress2005Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintformat2005isbn-13978-0-511-13039-7e
6、Book(NetLibrary)isbn-100-511-13039-2eBook(NetLibrary)isbn-13978-0-521-83166-6hardbackisbn-100-521-83166-0hardbackisbn-13978-0-521-53937-1paperbackisbn-100-521-53937-4paperbackCambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofurlsforexternalorthird-partyinternet
7、websitesreferredtointhispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.Tothemostenthusiasticwriterever–mysonRadek.ContentsPrefacepagexi1Preliminaries,notationsandconventions11.1Elementsoftopology11.2Measuretheory31.3Functionsofbounde
8、dvariation.Riemann–
