[r._m._dudley]_real_analysis_and_probability_(camb(bookfi.org)

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1、ThispageintentionallyleftblankREALANALYSISANDPROBABILITYThismuchadmiredtextbook,nowreissuedinpaperback,offersaclearexpo-sitionofmodernprobabilitytheoryandoftheinterplaybetweenthepropertiesofmetricspacesandprobabilitymeasures.Thefirsthalfofthebookgivesanex

2、positionofrealanalysis:basicsettheory,generaltopology,measuretheory,integration,anintroductiontofunc-tionalanalysisinBanachandHilbertspaces,convexsetsandfunctions,andmeasureontopologicalspaces.Thesecondhalfintroducesprobabilitybasedonmeasuretheory,includ

3、inglawsoflargenumbers,ergodictheorems,thecentrallimittheorem,conditionalexpectations,andmartingaleconver-gence.AchapteronstochasticprocessesintroducesBrownianmotionandtheBrownianbridge.Theneweditionhasbeenmadeevenmoreself-containedthanbefore;itnowinclude

4、searlyinthebookafoundationoftherealnumbersystemandtheStone-Weierstrasstheoremonuniformapproximationinalgebrasoffunctions.Severalothersectionshavebeenrevisedandimproved,andtheextensivehistoricalnoteshavebeenfurtheramplified.Anumberofnewexercises,andhintsfo

5、rsolutionofoldandnewones,havebeenadded.R.M.DudleyisProfessorofMathematicsattheMassachusettsInstituteofTechnologyinCambridge,Massachusetts.CAMBRIDGESTUDIESINADVANCEDMATHEMATICSEditorialBoard:B.Bollobas,W.Fulton,A.Katok,F.Kirwan,P.SarnakAlreadypublished17W

6、.Dicks&M.DunwoodyGroupsactingongraphs18L.J.Corwin&F.P.GreenleafRepresentationsofnilpotentLiegroupsandtheirapplications19R.Fritsch&R.PiccininiCellularstructuresintopology20H.KlingenIntroductorylecturesonSiegelmodularforms21P.KoosisThelogarithmicintegralII

7、22M.J.CollinsRepresentationsandcharactersoffinitegroups24H.KunitaStochasticflowsandstochasticdifferentialequations25P.WojtaszczykBanachspacesforanalysts26J.E.Gilbert&M.A.M.MurrayCliffordalgebrasandDiracoperatorsinharmonicanalysis27A.Frohlich&M.J.TaylorAlge

8、braicnumbertheory28K.Goebel&W.A.KirkTopicsinmetricfixedpointtheory29J.F.HumphreysReflectiongroupsandCoxetergroups30D.J.BensonRepresentationsandcohomologyI31D.J.BensonRepresentationsandcohomologyII32C.Allday&V.PuppeCohomologi