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1、MeasureTheoryandFinePropertiesofFunctions@)CRCPRESSSTUDIESINADVANCEDMATHEMATICSLibraryofCongressCataloging-in-PublicationDataEvans,LawrenceC.,1949-MeasuretheoryandfinepropertiesoffunctionsIbyLawrenceC.EvansandRonaldF.Gariepy.p.em.Includesbibliographicalreferencesandindex.ISBN0-8493-7157-0I.Measure
2、Theory.2.FunctionalAnalysis.I.Gariepy,RonaldF.II.Title.QA325.E9219925!5'.42--dc2091-30277CIPThisbookrepresentsinformationobtainedfromauthenticandhighlyregardedsources.Reprintedmaterialisquotedwithpermission,andsourcesareindicated.Awidevarietyofreferencesarelisted.Everyreasonableefforthasbeenmadeto
3、givereliabledataandinformation,buttheauthorandthepublishercannotassumeresponsibilityforthevalidityofallmaterialsorfortheconsequencesoftheiruse.Allrightsreserved.Thisbook,oranypartsthereof,maynotbereproducedinanyformwithoutwrittenconsentfromthepublisher.ThisbookwasformattedwithIbTJ?(byArchetypePubl
4、ishingInc.,P.O.Box6567,Champaign,IL6!82I.DirectallinquiriestoCRCPress,Inc.,2000CorporateBlvd.,N.W.,BocaRaton,Florida,33431.©1992byCRCPress,Inc.InternationalStandardBookNumber0-8493-7157-0PrintedintheUnitedStatesofAmericaI234567890-���--�--------Contents..PrefaceVll1GeneralMeasureTheory11.1Measures
5、andmeasurablefunctionsI1.2Lu'sin'sandEgoroff'sTheorems131.3Integralsandlimittheorems171.4Productmeasures,Fubini'sTheorem,Lebesguemeasure221.5Coveringtheorems261.6DifferentiationofRadonmeasures371.7Lebesguepoints;Approximatecontinuity431.8RieszRepresentationTheorem491.9Weakconvergenceandcompactness
6、forRadonmeasures542HausdorffMeasure602.1Definitionsandelementaryproperties;Hausdorffdimension602.2IsodiametricInequality;71n=Ln652.3Densities712.4Hausdorffmeasureandelementarypropertiesoffunctions753AreaandCoareaFormulas793.1Lipschitzfunctions,Rademacher'sTheorem793.2LinearmapsandJacobians863.3The
7、AreaFormula923.4TheCoareaFormula104ViContents4SobolevFunctions1204.1Definitionsandelementaryproperties1204.2Approximation1224.3Traces1334.4Extensions1354.5Sobolevinequalities1384.6Compactness1444.7Capacity1464.8Q
