实分析和抽象分析

图书标准信息

• 作者 [美]休伊特（Hewitt E.） 著
• 出版社 世界图书出版公司
• 出版时间 2009-04
• 版次 1
• ISBN 9787510004476
• 定价 45.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 476页

【内容简介】

Thisbookisfirstofalldesignedasatextforthecourseusuallycalled"theoryoffunctionsofarealvariable".ThiscourseisatpresentcustomarilyofferedasafirstorsecondyeargraduatecourseinUnitedStatesuniversities，althoughtherearesignsthatthissortofanalysiswillsoonpenetrateupperdivisionundergraduatecurricula.Wehaveincludedeverytopicthatwethinkessentialforthetrainingofanalysts，andwehavealsogonedownanumberofinterestingbypaths.Wehopetoothatthebookwillbeusefulasareferenceformaturemathematiciansandotherscientificworkers.Hencewehavepresentedverygeneralandcompleteversionsofanumberofimportanttheoremsandconstructions.Sincethesesophisticatedversionsmaybedifficultforthebeginner，weavegivenelementaryavatarsofallimportanttheorems，withappropriatesuggestionsforskipping.Wehavegivencompletedefinitions，explanations，andproofsthroughout，sothatthebookshouldbeusableforindividualstudyaswellasforacoursetext

【目录】

ChapterOne：SetTheoryandAlgebra

Section1.Thealgebraofsets

Section2.Relationsandfunctions

Section3.Theaxiomofchoiceandordinalnumbers

Section4.Cardinalnumbersandordinalnumbers

Section5.Constructionoftherealandcomplexnumberfields

ChapterTwo：TopologyandContinuousFunctions

Section8.Theriemann-Stieltjesintegral

Section9.Extendingcertainfunctionals

Section10.Measuresandmeasurablesets

Section11.Measurablefunctions

Section12.TheabstractLebesgueintegral

ChapterFour：FunctionSpacesandBanachSpaces

Section13.Thespaces

Section14.AbstractBanachspaces

Section15.Theconjugatespace

Section16.AbstractHilbertspaces

ChapterFive：Differentiation

Section17.Differentiableandnondifferentiablefunctions

Section18.Absolutelycontinuousfunctions

Section19.ComplexmeasuresandtheLEBESGUE-RADON-NIKODYMtheorem

Section20.ApplicationsoftheLEBESGUE-RADON-NIKODYMtheorem

ChapterSix：IntegrationonProductSpaces

Section21.Theproductoftwomeasurespaces

Section22.Productsofinfinitelymanymeasurespaces

IndexofSymbols

IndexofAuthorsandTerms