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1、ProbabilityandItsApplicationsAseriespublishedinassociationwiththeAppliedProbabilityTrustEditors:J.Gani,C.C.Heyde,T.G.KurtzOlavKallenbergProbabilisticSymmetriesandInvariancePrinciplesOlavKallenbergDepartmentofMathematicsandStatisticsAuburnUniversityAuburn,A
2、L36849-5310USAkalleoh@auburn.eduSeriesEditorsJ.GaniC.C.HeydeT.G.KurtzStochasticAnalysisGroup,StochasticAnalysisGroup,DepartmentofCMACMAMathematicsAustralianNationalAustralianNationalUniversityofWisconsinUniversityUniversity480LincolnDriveCanberraACT0200Can
3、berraACT0200Madison,WI53706AustraliaAustraliaUSAMathematicsSubjectClassification(2000):60G09,60-02LibraryofCongressControlNumber:2005923579ISBN-10:0-387-25115-4Printedonacid-freepaper.ISBN-13:978-0387-25115-8©2005SpringerScience+BusinessMedia,Inc.Allrights
4、reserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,Inc.,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwith
5、anyformofinformationstorageandretrieval,electronicadapta-tion,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevel-opedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentified
6、assuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.(MP)987654321springeronline.comPrefaceThisbookisaboutrandomobjects—sequences,processes,arrays,measures,functionals—withinteresti
7、ngsymmetryproperties.Heresymmetryshouldbeunderstoodinthebroadsenseofinvarianceunderafamily(notnecessarilyagroup)ofmeasurabletransformations.Tobeprecise,itisnottherandomobjectsthemselvesbutrathertheirdistributionsthatareassumedtobesymmetric.Thoughmanyprobab
8、ilisticsymmetriesareconceivableandhavebeenconsideredinvariouscontexts,fourofthem—stationarity,contractability,exchangeability,androtatability—standoutasespeciallyinterestingandim-portantinseveralways:Theirstu
