实分析和抽象分析 【正版图书】 mobi 下载 网盘 caj lrf pdf txt 阿里云

《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 functi*** 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 ***ysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of ***ysts, 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 versi*** of a number of important theorems and c***tructi***. Since these sophisticated versi*** may be difficult for the beginner, we ave given elementary avatars of all important theorems, with appropriate suggesti*** for skipping. We have given complete definiti***, explanati***, 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.Relati***andfuncti***

Section3.Theaxiomofchoiceandordinalnumbers

Section4.Cardinalnumbersandordinalnumbers

Section5.C***tructionoftherealandcomplexnumberfields

ChapterTwo TopologyandContinuousFuncti***

Section8.Theriemann-Stieltjesintegral

Section9.Extendingcertainfunctionals

Section0.Measuresandmeasurablesets

Section.Measurablefuncti***

Section2.TheabstractLebesgueintegral

ChapterFour FunctionSpacesandBanachSpaces

Section3.Thespaces

Section4.AbstractBanachspaces

Section5.Theconjugatespace

Section6.AbstractHilbertspaces

ChapterFive Differentiation

Section7.Differentiableandnondifferentiablefuncti***

Section8.Absolutelycontinuousfuncti***

Section9.ComplexmeasuresandtheLEBESGUE-RADON-NIKODYMtheorem

Section20.Applicati***oftheLEBESGUE-RADON-NIKO

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Thisbookisfirstofalldesignedasatextforthecourseusuallycalledtheoryoffuncti***ofarealvariable.ThiscourseisatpresentcustomarilyofferedasafirstorsecondyeargraduatecourseinUnitedStatesuniversities，althoughtherearesignsthatthissortof***ysiswillsoonpenetrateupperdivisionundergraduatecurricula.Weheincludedeverytopicthatwethinkessentialforthetrainingof***ysts，andwehealsogonedownanumberofinterestingbypaths.Wehopetoothatthebookwillbeusefulasareferenceformaturemathematiciansandotherscientificworkers.Hencewehepresentedverygeneralandcompleteversi***ofanumberofimportanttheoremsandc***tructi***.Sincethesesophisticatedversi***maybedifficultforthebeginner，weegivenelementaryatarsofallimportanttheorems，withappropriatesuggesti***forskipping.Wehegivencompletedefiniti***，explanati***，andproofsthroughout，sothatthebookshouldbeusableforindividualstudyaswellasforacoursetext

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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 functi*** 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 ***ysis will soon penetrate upper division undergraduate curricula. We have included every topic that we think essential for the training of ***ysts, 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 versi*** of a number of important theorems and c***tructi***. Since these sophisticated versi*** may be difficult for the beginner, we ave given elementary avatars of all important theorems, with appropriate suggesti*** for skipping. We have given complete definiti***, explanati***, and proofs throughout, so that the book should be usable for individual study as well as for a course text