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《实分析和抽象分析》讲述了：This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present customarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner, we ave given elementary avatars of all important theorems, with appropriate suggestions for skipping. We have given complete definitions, explanations, and proofs throughout, so that the book should be usable for individual study as well as for a course text

ChapterOne SetTheoryandAlgebra

Section.Thealgebraofsets

Section2.Relationsandfunctions

Section3.Theaxiomofchoiceandordinalnumbers

Section4.Cardinalnumbersandordinalnumbers

Section5.Constructionoftherealandcomplexnumberfields

ChapterTwo TopologyandContinuousFunctions

Section8.Theriemann-Stieltjesintegral

Section9.Extendingcertainfunctionals

Section0.Measuresandmeasurablesets

Section.Measurablefunctions

Section2.TheabstractLebesgueintegral

ChapterFour FunctionSpacesandBanachSpaces

Section3.Thespaces

Section4.AbstractBanachspaces

Section5.Theconjugatespace

Section6.AbstractHilbertspaces

ChapterFive Differentiation

Section7.Differentiableandnondifferentiablefunctions

Section8.Absolutelycontinuousfunctions

Section9.ComplexmeasuresandtheLEBESGUE-RADON-NIKODYMtheorem

Section20.ApplicationsoftheLEBESGUE-RADON-NIKO

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Thisbookisfirstofalldesignedasatextforthecourseusuallycalledtheoryoffunctionsofarealvariable.ThiscourseisatpresentcustomarilyofferedasafirstorsecondyeargraduatecourseinUnitedStatesuniversities，althoughtherearesignsthatthissortofanalysiswillsoonpenetrateupperdivisionundergraduatecurricula.Weheincludedeverytopicthatwethinkessentialforthetrainingofanalysts，andwehealsogonedownanumberofinterestingbypaths.Wehopetoothatthebookwillbeusefulasareferenceformaturemathematiciansandotherscientificworkers.Hencewehepresentedverygeneralandcompleteversionsofanumberofimportanttheoremsandconstructions.Sincethesesophisticatedversionsmaybedifficultforthebeginner，weegivenelementaryatarsofallimportanttheorems，withappropriatesuggestionsforskipping.Wehegivencompletedefinitions，explanations，andproofsthroughout，sothatthebookshouldbeusableforindividualstudyaswellasforacoursetext

书籍介绍

《实分析和抽象分析》讲述了：This book is first of all designed as a text for the course usually called "theory of functions of a real variable". This course is at present customarily offered as a first or second year graduate course in United States universities, although there are signs that this sort of analysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of analysts, and we have also gone down a number of interesting bypaths. We hope too that the book will be useful as a reference for mature mathematicians and other scientific workers. Hence we have presented very general and complete versions of a number of important theorems and constructions. Since these sophisticated versions may be difficult for the beginner, we ave given elementary avatars of all important theorems, with appropriate suggestions for skipping. We have given complete definitions, explanations, and proofs throughout, so that the book should be usable for individual study as well as for a course text