[John_Lamperti]_Probability_A_Survey_of_the_Mathematical.Sciences

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1、ThispageintentionallyleftblankProbabilityWILEYSERIESINPROBABILITYANDSTATISTICSEstablishedbyWALTERA.SHEWHARTandSAMUELS.WILKSEditors:VicBarnett,RalphA.Bradley,NicholasI.Fisher,J.StuartHunter,J.B.Kadane,DavidG.Kendall,DavidW.Scott,AdrianF.M.Smith,JozefL.

2、Teugels,GeoffreyS.WatsonAcompletelistofthetitlesinthisseriesappearsattheendofthisvolumeProbabilityASurveyoftheMathematicalTheorySecondEditionJOHNW.LAMPERTIWileySeriesinProbabilityandStatisticsAWiley-IntersciencePublicationJOHNWILEY&SONS,INC.NewYork•Ch

3、ichester•Brisbane•Toronto•SingaporeThistextisprintedonacid-freepaper.Copyright©1996byJohnWiley&Sons,Inc.Allrightsreserved.PublishedsimultaneouslyinCanada.ReproductionortranslationofanypartofthisworkbeyondthatpermittedbySection107or108ofthe1976UnitedSt

4、atesCopyrightActwithoutthepermissionofthecopyrightownerisunlawful.RequestsforpermissionorfurtherinformationshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,605ThirdAvenue,NewYork,NY10158-0012.LibraryofCongressCataloginginPublicationData

5、:Lamperti,J.(John)Probability:asurveyofthemathematicaltheory/JohnW.Lamperti.—2nded.p.cm.—(Wileyseriesinprobabilityandstatistics)"AWileyIntersciencepublication."Includesbibliographicalreferences(p.-)andindex.ISBN13:978-0-471-15407-51.Probabilities.I.Ti

6、tle.II.Series:Wileyseriesinprobabilityandstatistics.Probabilityandstatistics.QA273.L261996519.2—dc2096-955910987654321ContentsPreface1.Foundations1.ProbabilitySpaces,12.RandomVariablesandTheirExpectations,53.Independence,124.ConditionalExpectationsand

7、Probabilities,175.WhenDoRandomVariablesExist?262.LawsofLargeNumbersandRandomSeries6.TheWeakLawofLargeNumbers,317.TheWeierstrassApproximationTheorem,388.TheStrongLawofLargeNumbers,419.TheStrongLaw—Continued,4410.ConvergenceofRandomSeries,5211.MoreonInd

8、ependence;the0-1Law,5712.TheLawoftheIteratedLogarithm,613.LimitingDistributionsandtheCentralLimitProblem13.WeakConvergenceofMeasures,7114.TheMaximumofaRandomSample,7815.CharacteristicFunctions,8116.TheCentralLimitTheorem,9417.StableDistributio