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1、BasicElementsofRealAnalysisMurrayH.ProtterSpringerMurrayH.ProtterDepartmentofMathematicsUniversityofCaliforniaBerkeley,CA94720USAEditorialBoardS.AxlerF.W.GehringK.A.RibetMathematicsDepartmentMathematicsDepartmentDepartmentofSanFranciscoStateEastHallMathematicsUniversityUniv
2、ersityofMichiganUniversityofCaliforniaSanFrancisco,CA94132AnnArbor,MI48109atBerkeleyUSAUSABerkeley,CA94720-38USAFrontcoverillustration:fconvergestof,butf1fdoesnotconvergetof1f.(Seep.167ofn0n0textforexplanation.)MathematicsSubjectClassification(1991):26-01,26-06,26A54Library
3、ofCongressCataloging-in-PublicationDataProtter,MurrayH.Basicelementsofrealanalysis/MurrayH.Protter.p.cm.—(Undergraduatetextsinmathematics)Includesbibliographicalreferencesandindex.ISBN0-387-98479-8(hardcover:alk.paper)1.Mathematicalanalysis.I.Title.II.Series.QA300.P96781998
4、515—dc2198-16913c1998Springer-VerlagNewYork,Inc.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(Springer-VerlagNewYork,Inc.,175FifthAvenue,NewYork,NY10010,USA),exceptforbriefexcerptsinconnectionwithreviewsorschol
5、arlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseofgeneraldescriptivenames,tradenames,trademarks,etc.,inthispublication,eveniftheform
6、erarenotespeciallyidentified,isnottobetakenasasignthatsuchnames,asunderstoodbytheTradeMarksandMerchandiseMarksAct,mayaccordinglybeusedfreelybyanyone.ISBN0-387-98479-8Springer-VerlagNewYorkBerlinHeidelbergSPIN10668224ToBarbaraandPhilip..........................Preface........
7、.........SometimeagoCharlesB.MorreyandIwroteAFirstCourseinRealAnaly-sis,abookthatprovidesmaterialsufficientforacomprehensiveone-yearcourseinanalysisforthosestudentswhohavecompletedastandardele-mentarycourseincalculus.Thebookhasbeenthroughtwoeditions,thesecondofwhichappearedi
8、n1991;smallchangesandcorrectionsofmis-printshavebeenmadeinthefifthprintingoftheseco
