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1、ACOURSEINPROBABILITYTHEORYTHIRDEDITIONACOURSEINPROBABILITYTHEORYTHIRDEDITIONKaiLaiChungStanfordUniversity@f.CADEl-fICPRESS--"------p,:-il1rcJurtSCIenceandTechnologyCompanySanDiegoSailFranciscoNewYorkBo"lollLondonSydneyTokyoThisbookisprintedonacid-
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3、ONINWRITINGFROMTHEPUBLISHER.Requestsforpermissiontomakecopiesofanypartoftheworkshouldbemailedtothefollowingaddress:PermissionsDepartment,Harcourt,Inc.,6277SeaHarborDrive,Orlando,Florida32887-6777.ACADEMICPRESSAHarcourtScienceandTechnologyCompany525BS
4、treet,Suite1900,SanDiego,CA92101-4495,USAhttp://www.academicpress.comACADEMICPRESSHarcourtPlace,32JamestownRoad,London,NW17BY,UKhttp://www.academicpress.comLibraryofCongressCataloginginPublicationDat:l:00-106712InternationalStandardBookNumber:0-12-17
5、4151-6PRINTEDINTHEUNITEDSTATESOFAMERICA00010203IP987654321ContentsPrefacetothethirdeditionixPrefacetothesecondeditionxiPrefacetothefirsteditionX1111IDistributionfunction1.1Monotonefunctions11.2Distributionfunctions71.3Absolutelycontinuousandsingt.;ll
6、ardistributions112IMeasuretheory2.1Classesofsets162.2Probabilitymeasuresandtheirdistributionfunctions213IRandomvariable.Expectation.Independence3.1Generaldefinitions343.2Propertiesofmathematicalexpectation413.3Independence534IConvergenceconcepts4.1Va
7、riousmodesofconvergence684.2Almostsureconvergence;Borel-Cantellilemma75viICONTENTS4.3Vagueconvergence844.4Continuation914.5Uniformintegrability;convergenceofmoments995ILawoflargenumbers.Randomseries5.1Simplelimittheorems1065.2Weaklawoflargenumbers112
8、5.3Convergenceofseries1215.4Stronglawoflargenumbers1295.5Applications138BibliographicalNote1486ICharacteristicfunction6.1Generalproperties;convolutions1506.2Uniquenessandinversion1606.3Convergencetheorems1696.4Simpleapplications1756.5Representationth
