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1、ProbabilitywithMartingalesDavidWilliamsStatisticalLaboratory,DPMMSCambridgeUniversityTh�rightofth�Univ�rsityofCambridg�toprintandu/1allmannerofbookswasgrantedbyHenryVIIIin1534.TheUniv�rsityhasprintedandpublishedcontinuouslysince/584.CAMBRIDGEUNIVERSITYPRESSCambridgeNewYorkPor
2、tChesterMelbourneSydneyPublishedbythePressSyndicateoftheUniversityofCambridgeThePittBuilding,TrumpingtonStreet,CambridgeCB21RP40West20thStreet,NewYork,NY10011,USA10,StamfordRoad,Oakleigh,Melbourne3166,Australia©CambridgeUniversityPress1991PrintedinGreatBritainattheUniversityP
3、ress,CambridgeBritishLibrarycataloguinginpublicationdataavailableLibraryofCongresscataloginginpublicationdataavailableContentsPreface-pleaseread!XI...AQuestionofTern1inologyXlllAGuidetoNotationXlVChapter0:ABranching-ProcessExan1ple10.0.Introductoryremarks.0.1.Typicalnumberofc
4、hildren,X.0.2.Sizeofnthgeneration,Zn.0.3.Useofconditionalexpectations.0.4.Extinctionprobability,1r.0.5.Pauseforthought:measure.0.6.Ourfirstmartingale.0.7.Convergence(ornot)ofexpectations.0.8.FindingthedistributionofM00•0.9.Concreteexample.PARTA:FOUNDATIONSChapter1:MeasureSpac
5、es141.0.Introductoryremarks.1.1.Definitionsofalgebra,a-algebra.1.2.Examples.Borela-algebras,ses),B=BeR).1.3.Definitionsconcerningsetfunctions.1.4.Definitionofmeasurespace.1.5.Definitionsconcerningmeasures.1.6.Lemma.Uniquenessofextension,1r-systems.1.7.Theorem.Caratheodory'sex
6、tensiontheorem.1.8.LebesguemeasureLeboneeo,1],seo,1]).1.9.Lemma.Elementaryinequalities.1.10.Lemma.Monotone-convergencepropertiesofmeasures.1.11.Example/Warning.Chapter2:Events232.1.Modelforexperiment:en,F,P).2.2.Theintuitivemeaning.2.3.Examplesofen,F)pairs.2.4.Almostsurelyea.
7、s.)2.5.Reminder:limsup,liminf,!lim,etc.2.6.Definitions.limsupEn,(En,i.o.).2.7.vVlContentsFirstBorel-CantelliLemma(BC1).2.8.Definitions.liminfEn,(En,ev).2.9.Exercise.Chapter3:RandomVariables293.1.Definitions.E-measurablefunction,mE,(mE)+,bE.3.2.ElementaryPropositionsonmeasurab
8、ility.3.3.Lemma.Sumsandproductsofmeasurablefunctionsaremeasurable.3.
