- 实分析与泛函分析(第3版影印版)(英文版)
- - 作者：(美)S.朗|责编:高蓉//李黎
  - 出版社：世界图书出版公司
  - ISBN：9787506233071
  - 出版日期：2001/01/01
  - 页数：580
- 售价：59.6

内容大纲
    本书是Springer《数学研究生教材》第142卷（GTM142），初版于1991年，这是第3版。
    本书内容包括现代实分析与泛函分析基础理论，全书分6部分，共23章。
    本书的读者对象为数学及有关专业的研究生和科研人员。
作者介绍
目录
PART ONE  General Topology
  CHAPTER I  Sets
    §1.Some Basic Terminology
    §2.Denumerable Sets
    §3.Zorn's Lemma
  CHAPTER II  Topological Spaces
    §1.Open and Closed Sets
    §2.Connected Sets
    §3.Compact Spaces
    §4.Separation by Continuous Functions
    §5.Exercises
  CHAPTER III  Continuous Functions on Compact Sets
    §1.The Stone-Weierstrass Theorem
    §2.Ideals of Continuous Functions
    §3.Ascoli's Theorem
    §4.Exercises
PART TWO  Banach and Hilbert Spaces
  CHAPTER IV  Banach Spaces
    §1.Definitions, the Dual Space, and the Hahn-Banach Theorem
    §2.Banach Algebras
    §3.The Linear Extension Theorem
    §4.Co mpletion of a Normed Vector Space
    §5.Spaces with Operators
      Appendix: Convex Sets
      1.The Krein-Milman Theorem
      2.Mazur's Theorem
    §6.Exercises
  CHAPTER V  Hilbert Space
    §1.Hermitian Forms
    §2.Functionals and Operators
    §3.Exercises
PART THREE  Integration
  CHAPTER VI  The General integral
    §1.Measured Spaces, Measurable Maps, and Positive Measures
    §2.The Integral of Step Maps
    §3.The L1-Completion
    §4.Properties of the Integral: First Part
    §5.Properties of the Integral: Second Part
    §6.Approximations
    §7.Extension of Positive Measures from Algebras to σ-Algebras
    §8.Product Measures and Integration on a Product Space
    §9.The Lebesgue Integral in Rp
    §10.Exercises
  CHAPTER VII  Duality and Representation Theorems
    §1.The Hilbert Space L2(u)
    §2.Duality Between L1(μ) and L∞(μ)
    §3.Complex and Vectorial Measures
    §4.Complex or Vectorial Measures and Duality
    §5.The LP Spaces, 1
    §6.The Law of Large Numbers

    §7.Exercises
  ……
PART FOUR  Calculus
PART FIVE  Functional Analysis
PART SIX  Global Analysis
Bibliography
table of notation
index

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