资源描述：
《Real Analysis Measure Theory, Integration, and Hilbert Spaces (2005)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、REALANALYSISIbookrootOctober20,2007PrincetonLecturesinAnalysisIFourierAnalysis:AnIntroductionIIComplexAnalysisIIIRealAnalysis:MeasureTheory,Integration,andHilbertSpacesIVFunctionalAnalysis:IntroductiontoFurtherTopicsinAnalysisPrincetonLecturesinAnalysisIIIREALANALYSISMeasureTheory,Integ
2、ration,andHilbertSpacesEliasM.Stein&RamiShakarchiPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDCopyright©2005byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordStreet,Woodstock,OxfordshireO
3、X201TWAllRightsReservedLibraryofCongressControlNumber2004114065ISBN978-0-691-11386-9BritishLibraryCataloging-in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-readycopyfromwhichthisbookwasprintedPrintedonacid-freepaper.∞press.prin
4、ceton.eduPrintedintheUnitedStatesofAmerica357910864TomygrandchildrenCarolyn,Alison,JasonE.M.S.TomyparentsMohamed&MireilleandmybrotherKarimR.S.ForewordBeginninginthespringof2000,aseriesoffourone-semestercoursesweretaughtatPrincetonUniversitywhosepurposewastopresent,inanintegratedmanner,t
5、hecoreareasofanalysis.Theobjectivewastomakeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoillustratethewideapplicabilityofideasofanalysistoother¯eldsofmathematicsandscience.Thepresentseriesofbooksisanelaborationofthelecturesthatweregiven.Whilethereareanumberofexce
6、llenttextsdealingwithindividualpartsofwhatwecover,ourexpositionaimsatadi®erentgoal:pre-sentingthevarioussub-areasofanalysisnotasseparatedisciplines,butratherashighlyinterconnected.Itisourviewthatseeingtheserelationsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstand
7、ingofthesubjectasawhole.Withthisoutcomeinmind,wehaveconcentratedonthemainideasandtheoremsthathaveshapedthe¯eld(sometimessacri¯cingamoresystematicapproach),andwehavebeensensitivetothehistoricalorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofourvolumes,
