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1、SECONDEDITIONDanielW.StroockAConciseIntroductiontotheTheoryofIntegrationsecondeditionBirkhauserBoston•Basel•Berlin1994DanielW.StroockDepartmentofMathematicsMassachusettsInstituteofTechnologyCambridge,MA02139LibraryofCongressCataloging-in-PublicationDataStroock,DanielM.A
2、conciseintroductiontothetheoryofintegrationIDanielW.Stroock.--2nded.p.em.Includesindex.ISBN0-8176-3759-1(acid-freepaper)1.Integrals,Generalized.2.MeasureTheory.I.Title.QA312.S78199494-6246512'.4--dc20CIPPrintedonacid-freepaperBirkhiiuser$®©secondedition1994DanielW.Stroo
3、ckFirstedition:WorldScientific,SingaporeCopyrightisnotclaimedforworksofU.S.Governmentemployees.Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,
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5、toCCC,222RosewoodDrive,Danvers,MA01923,U.S.A.SpecialrequestsshouldbeaddresseddirectlytoBirkhauserBoston,675MassachusettsAvenue,Cambridge,MA02139,U.S.A.ISBN0-8176-3759-1ISBN3-7643-3759-1TypesetbytheAuthor.PrintedandboundbyQuinn-Woodbine,Woodbine,NJ.PrintedintheU.S.A.9876
6、54321ContentsPreface..............VllChapter1:TheClassicalTheory.....11.1:RiemannIntegration....11.2:Riemann-StieltjesIntegration7ChapterII:Lebesgue'sMeasure...192.0:TheIdea..............192.1:Existence.....212.2:EuclideanInvariance30ChapterIll:LebesgueIntegration......
7、....343.1:MeasureSpaces.................343.2:ConstructionofIntegrals...............403.3:ConvergenceofIntegrals.......503.4:Lebesgue'sDifferentiationTheorem......62ChapterIV:ProductsofMeasures..........684.1:Fubini'sTheorem.................684.2:SteinerSymmetrizationan
8、dtheIsodiametricInequality.74ChapterV:ChangesofVariable...............805.0:Introduction...................805
