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1、REALANDCOMPLEXANALYSISREALANDCOMPLEXANALYSISThirdEditionWalterRudinProfessorofMathematicsUniversityofWisconsin,Madison)McGraw-HillBookCompanyNewYorkSt.LouisSanFranciscoAucklandBogotaHamburgLondonMadridMexicoMilanMontrealNewDelhiPanamaParisSaoPauloSingaporeS
2、ydneyTokyoTorontoREALANDCOMPLEXANALYSISINTERNATIONALEDITION1987ExclusiverightsbyMcGraw-HillBookCo.,Singaporeformanufactureandexport.Thisbookcannotbere-exportedfromthecountrytowhichitisconsignedbyMcGraw-Hill.012345678920BJE9876Copyright©1987,1974,1966byMcGra
3、w-Hill,Inc.Allrightsreserved.Nopartofthispublicationmaybereproducedordistributedinanyformorbyanymeans,orstoredinadatabaseoraretrievalsystem,withoutthepriorwrittenpermissionofthepublisher.ThisbookwassetinTimesRoman.TheeditorwasPeterR.Devine.Theproductionsupe
4、rvisorwasDianeRenda.LibraryofCongressCataloging-in-PublicationDataRudin,Walter,1921-Realandcomplexanalysis.Bibliography:p.Includesindex.1.Mathematicalanalysis.I.Title.QA300.R82198751586-7ISBN0-07-054234-1WhenorderingthistitleuseISBN0-07-100276-6PrintedinSin
5、gaporeABOUTTHEAUTHORWalterAnalysis,RudinRealandistheComplexauthorAnalofysis,threetextbooks,PrinciplesofMathematicalandFunctionalAnalysis,whosewidespreaduseisillustratedbythefactthattheyhavebeentranslatedintoatotalof13languages.Hewrotethefirstofthesewhilehew
6、asaC.L.E.MooreInstructoratM.I.T.,justtwoyearsafterreceivinghisPh.D.atDukeUniversityin1949.LaterhetaughtattheUniversityofRochester,andisnowaVilasResearchProfessorattheUniversityofWisconsin-Madison,wherehehasbeensince1959.HehasspentleavesatYaleUniversity,atth
7、eUniversityofCaliforniainLaJolla,andattheUniversityofHawaii.HisresearchhasdealtmainlywithharmonicanalysisandwithcomplexvariAnaables.lysiHesonhasGroups,writtenFunctithreeonTheorresearchyinmonographsPolydiscs,onthesetopics,FourierUnitBallofC0•andFunctionTheor
8、yintheCONTENTSPrefaceXlllPrologue:TheExponentialFunction1Chapter1AbstractIntegration5Set-theoreticnotationsandterminology6Theconceptofmeasurability8Simplefunctions15Elementarypropertiesofmeasures16Arit
