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实分析和抽象分析书籍详细信息
- ISBN：9787510004476
- 作者：暂无作者
- 出版社：暂无出版社
- 出版时间：2009-04
- 页数：476
- 价格：105.81
- 纸张：胶版纸
- 装帧：平装
- 开本：16开
- 语言：未知
- 丛书：暂无丛书
- TAG：暂无
- 豆瓣评分：暂无豆瓣评分
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内容简介：
《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
书籍目录：
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
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