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1、TheErgodicTheoryofDiscreteSamplePathsPaulC.ShieldsGraduateStudiesinMathematicsVolume13AmericanMathematicalSocietyEditorialBoardJamesE.HumphreysDavidSattingerJuliusL.ShanesonLanceW.Small,chair1991MathematicsSubjectClassification.Primary28D20,28D05,94A17;Secondary60F05,60G17,94A24.AB
2、STRACT.Thisbookisaboutfinite-alphabetstationaryprocesses,whichareimportantinphysics,engineering,anddatacompression.Thebookisdesignedforuseingraduatecourses,sem-inarsorselfstudyforstudentsorfacultywithsomebackgroundinmeasuretheoryandprobabilitytheory.LibraryofCongressCataloging-in-P
3、ublicationDataShields,PaulC.Theergodictheoryofdiscretesamplepaths/PaulC.Shields.p.cm.—(Graduatestudiesinmathematics,ISSN1065-7339;v.13)Includesbibliographicalreferencesandindex.ISBN0-8218-0477-4(alk.paper)1.Ergodictheory.2.Measure-preservingtransformations.3.Stochasticprocesses.I.T
4、itle.II.Series.QA313.5551996519.2'32—dc2096-20186CIPCopyingandreprinting.Individualreadersofthispublication,andnonprofitlibrariesactingforthem,arepermittedtomakefairuseofthematerial,suchastocopyachapterforuseinteachingorresearch.Permissionisgrantedtoquotebriefpassagesfromthispublic
5、ationinreviews,providedthecustomaryacknowledgmentofthesourceisgiven.Republication,systematiccopying,ormultiplereproductionofanymaterialinthispublication(includingabstracts)ispermittedonlyunderlicensefromtheAmericanMathematicalSociety.RequestsforsuchpermissionshouldbeaddressedtotheA
6、ssistanttothePublisher,AmericanMathematicalSociety,P.O.Box6248,Providence,RhodeIsland02940-6248.Requestscanalsobemadebye-mailtoreprint-permission0ams.org.C)Copyright1996bytheAmericanMathematicalSociety.Allrightsreserved.TheAmericanMathematicalSocietyretainsallrightsexceptthosegrant
7、edtotheUnitedStatesGovernment.PrintedintheUnitedStatesofAmerica.®Thepaperusedinthisbookisacid-freeandfallswithintheguidelinesestablishedtoensurepermanenceanddurability...Printedt.,1onrecycledpaper.10987654321010099989796ContentsPrefaceixIBasicconcepts.1I.1Stationaryprocesses.11.2Th
8、eergodictheorymodel.131.3T
