【内容简介】: 　　作者Pugh在伯克利大学讲授数学分析课程30多年之久的基础上编写而成，书中语言表述生动活泼、通俗易懂，引用了很多有价值的例子以及来自Dieudonne，Littlewood和Osserman等几位数学家的评论，还精心挑选了500多个精彩的练习题。《实数学分析（影印版）》内容包括实数、拓扑知识初步、实变函数、函数空间、多元微积分、Lebesgue积分理论等，其中多元微积分的讲法较为接近当前数学界常用的语言，将会对我国数学分析的教学产生积极的影响。
【目录】: 1RealNumbers
1Preliminaries
2Cuts
3EuclideanSpace
4Cardinality
5*ComparingCardinalities
6*TheSkeletonofCalculus
Exercises
2ATasteofTopology
1MetricSpaceConcepts
2Compactness
3Connectedness
4Coverings
5CantorSets
6*CantorSetLore
7*Completion
Exercises
3FunctionsofaRealVariable
1Differentiation
2RiemannIntegration
3Series
Exercises
4FunctionSpaces
1UniformConvergenceandC0[a,b]
2PowerSeries
3CompactnessandEquicontinuityinCO
4UniformApproximationinCo
5ContractionsandODEs
6*AnalyticFunctions
7*NowhereDifferentiableContinuousFunctions
8*SpacesofUnboundedFunctions
Exercises
5MultivariableCalculus
1LinearAlgebra
2Derivatives
3Higherderivatives
4SmoothnessClasses
5ImplicitandInverseFunctions
6*TheRankTheorem
7*LagrangeMultipliers
8MultipleIntegrals
9DifferentialForms
10TheGeneralStokesFormula
11*TheBrouwerFixedPointTheorem
AppendixA:PerorationsofDieudonne
AppendixB:TheHistoryofCavalierisPrinciple
AppendixC:AShortExcursioninto
theComplexField
AppendixD:PolarForm
AppendixE:Determinants
Exercises
6LebesgueTheory
1Outermeasure
2Measurability
3Regularity
4Lebesgueintegrals
5Lebesgueintegralsaslimits
6ItalianMeasureTheory
7Vitalicoveringsanddensitypoints
8LebesguesFundamentalTheoremofCalculus
9LebesguesLastTheorem
AppendixA:TranslationsandNonmeasurablesets
AppendixB:TheBanach-TarskiParadox
AppendixC:Riemannintegralsasundergraphs
AppendixD:LittlewoodsThreePrinciples
AppendixE:Roundness
AppendixF:Money
SuggestedReading
Bibliography
Exercises
Index