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1、MathematicsTEXTBOOKSinMATHEMATICSTEXTBOOKSinMATHEMATICSMEASURETHEORYMEASURETHEORYMeasureTheoryandFinePropertiesofFunctions,RevisedEditionprovidesadetailedexaminationofthecentralasser-ANDFINEPROPERTIEStionsofmeasuretheoryinn-dimensionalEuclideanspace.Thebookemphasizestherolesof
2、Hausdorffmeasureandcapacityincharacterizingthefinepropertiesofsetsandfunctions.OFFUNCTIONSOFFUNCTIONSTopicscoveredincludeaquickreviewofabstractmeasureRevisedEditiontheory,theoremsanddifferentiationinℝn,Hausdorffmeasures,areaandcoareaformulasforLipschitzmappingsandrelatedANDcha
3、nge-of-variableformulas,andSobolevfunctionsaswellasfunctionsofboundedvariation.FINEPROPERTIESThetextprovidescompleteproofsofmanykeyresultsomittedfromotherbooks,includingBesicovitch’scoveringtheorem,Rademacher’stheorem(onthedifferentiabilitya.e.ofLipschitzfunctions),areaandcoar
4、eaformulas,theprecisestructureofSobolevandBVfunctions,theprecisestructureofsetsoffiniteperimeter,andAleksandrov’stheorem(onthetwicedifferentiabilitya.e.ofconvexfunctions).Thisrevisededitionincludescountlessimprovementsinnotation,format,andclarityofexposition.Alsonewareseverals
5、ectionsdescribingtheπ-λtheorem,weakcompactnesscriteriainL1,andYoungmeasuremethodsforweakconvergence.Inaddition,thebibliographyhasbeenupdated.Topicsarecarefullyselectedandtheproofsaresuccinct,butGariepyEvanscomplete.Thisbookprovidesidealreadingformathematiciansandforgraduatestu
6、dentsinpureandappliedmathematics.LawrenceC.EvansK23386RonaldF.Gariepywww.crcpress.comK23386_FM.indd43/17/1512:52PMMEASURETHEORYANDFINEPROPERTIESOFFUNCTIONSRevisedEditionK23386_FM.indd13/17/1512:52PMTEXTBOOKSinMATHEMATICSSeriesEditors:AlBoggessandKenRosenPUBLISHEDTITLESABSTRACT
7、ALGEBRA:ANINQUIRY-BASEDAPPROACHJonathanK.Hodge,StevenSchlicker,andTedSundstromABSTRACTALGEBRA:ANINTERACTIVEAPPROACHWilliamPaulsenADVANCEDCALCULUS:THEORYANDPRACTICEJohnSrdjanPetrovicADVANCEDLINEARALGEBRANicholasLoehrANALYSISWITHULTRASMALLNUMBERSKarelHrbacek,OlivierLessmann,andR
8、ichardO’DonovanAPPLIEDDIFFERENTIALEQUATIONS:THEPRIMARYCOURSEV
