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1、KrishnaB.AthreyaSoumendraN.LahiriMeasureTheoryandProbabilityTheoryKrishnaB.AthreyaSoumendraN.LahiriDepartmentofMathematicsandDepartmentofStatisticsDepartmentofStatisticsIowaStateUniversityIowaStateUniversityAmes,IA50011Ames,IA50011snlahiri@iastate.edukba@iastate.eduEditorialBoardGeorgeCasellaSteph
2、enFienbergIngramOlkinDepartmentofStatisticsDepartmentofStatisticsDepartmentofStatisticsUniversityofFloridaCarnegieMellonUniversityStanfordUniversityGainesville,FL32611-8545Pittsburgh,PA15213-3890Stanford,CA94305USAUSAUSALibraryofCongressControlNumber:2006922767ISBN-10:0-387-32903-Xe-ISBN:0-387-354
3、34-4ISBN-13:978-0387-32903-1Printedonacid-freepaper.©2006SpringerScience+BusinessMedia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexceptsinconne
4、ctionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyareno
5、tidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.(MVY)987654321springer.comDedicatedtoourwivesKrishnaS.AthreyaandPubaliBanerjeeandtothememoryofUmaManiAthreyaandNarayaniAmmalPrefaceThisbookaroseoutoftwograduat
6、ecoursesthattheauthorshavetaughtduringthepastseveralyears;thefirstonebeingonmeasuretheoryfollowedbythesecondoneonadvancedprobabilitytheory.Thetraditionalapproachtoafirstcourseinmeasuretheory,suchasinRoyden(1988),istoteachtheLebesguemeasureontherealline,thenthedifferentationtheoremsofLebesgue,Lp-space
7、sonR,anddogeneralmea-sureattheendofthecoursewithonemainapplicationtotheconstructionofproductmeasures.Thisapproachdoeshavethepedagogicadvantageofseeingoneconcretecasefirstbeforegoingtothegeneralone.Butthisalsohasth
