[stein-shakarchi] real analysis

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1、REALANALYSISIbookrootOctober20,2007PrincetonLecturesinAnalysisIFourierAnalysis:AnIntroductionIIComplexAnalysisIIIRealAnalysis:MeasureTheory,Integration,andHilbertSpacesIVFunctionalAnalysis:IntroductiontoFurtherTopicsinAnalysisPrincetonLecturesinAnalysisIIIREALANALY

2、SISMeasureTheory,Integration,andHilbertSpacesEliasM.Stein&RamiShakarchiPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDCopyright©2005byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversi

3、tyPress,6OxfordStreet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongressControlNumber2004114065ISBN978-0-691-11386-9BritishLibraryCataloging-in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-ready

4、copyfromwhichthisbookwasprintedPrintedonacid-freepaper.∞press.princeton.eduPrintedintheUnitedStatesofAmerica357910864TomygrandchildrenCarolyn,Alison,JasonE.M.S.TomyparentsMohamed&MireilleandmybrotherKarimR.S.ForewordBeginninginthespringof2000,aseriesoffourone-semes

5、tercoursesweretaughtatPrincetonUniversitywhosepurposewastopresent,inanintegratedmanner,thecoreareasofanalysis.Theobjectivewastomakeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoillustratethewideapplicabilityofideasofanalysistoother¯eldsofmat

6、hematicsandscience.Thepresentseriesofbooksisanelaborationofthelecturesthatweregiven.Whilethereareanumberofexcellenttextsdealingwithindividualpartsofwhatwecover,ourexpositionaimsatadi®erentgoal:pre-sentingthevarioussub-areasofanalysisnotasseparatedisciplines,butrath

7、erashighlyinterconnected.Itisourviewthatseeingtheserelationsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstandingofthesubjectasawhole.Withthisoutcomeinmind,wehaveconcentratedonthemainideasandtheoremsthathaveshapedthe¯eld(sometimessacri¯cingamo

8、resystematicapproach),andwehavebeensensitivetothehistoricalorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofourvolumes,