资源描述：
《real analysis (princeton lectures in analysis, volume 3) elias m. stein, rami shakarchi》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:IntroductiontoFurtherTopicsinAnalysisPrincetonLecturesinAnalysisIIIREALANALYSISMeasu
2、reTheory,Integration,andHilbertSpacesEliasM.Stein&RamiShakarchiPRINCETONUNIVERSITYPRESSPRINCETONANDOXFORDCopyright©2005byPrincetonUniversityPressPublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,NewJersey08540IntheUnitedKingdom:PrincetonUniversityPress,6OxfordS
3、treet,Woodstock,OxfordshireOX201TWAllRightsReservedLibraryofCongressControlNumber2004114065ISBN978-0-691-11386-9BritishLibraryCataloging-in-PublicationDataisavailableThepublisherwouldliketoacknowledgetheauthorsofthisvolumeforprovidingthecamera-readycopyfromwhichthisbookwas
4、printedPrintedonacid-freepaper.∞press.princeton.eduPrintedintheUnitedStatesofAmerica357910864TomygrandchildrenCarolyn,Alison,JasonE.M.S.TomyparentsMohamed&MireilleandmybrotherKarimR.S.ForewordBeginninginthespringof2000,aseriesoffourone-semestercoursesweretaughtatPrincetonU
5、niversitywhosepurposewastopresent,inanintegratedmanner,thecoreareasofanalysis.Theobjectivewastomakeplaintheorganicunitythatexistsbetweenthevariouspartsofthesubject,andtoillustratethewideapplicabilityofideasofanalysistoother¯eldsofmathematicsandscience.Thepresentseriesofboo
6、ksisanelaborationofthelecturesthatweregiven.Whilethereareanumberofexcellenttextsdealingwithindividualpartsofwhatwecover,ourexpositionaimsatadi®erentgoal:pre-sentingthevarioussub-areasofanalysisnotasseparatedisciplines,butratherashighlyinterconnected.Itisourviewthatseeingth
7、eserelationsandtheirresultingsynergieswillmotivatethereadertoattainabetterunderstandingofthesubjectasawhole.Withthisoutcomeinmind,wehaveconcentratedonthemainideasandtheoremsthathaveshapedthe¯eld(sometimessacri¯cingamoresystematicapproach),andwehavebeensensitivetothehistori
8、calorderinwhichthelogicofthesubjectdeveloped.Wehaveorganizedourexpositionintofourvolumes,
