- 测度论(影印版)(英文版)
- - 作者：(美)P.R.哈尔莫斯
  - 出版社：世图出版公司
  - ISBN：9787519255848
  - 出版日期：2019/03/01
  - 页数：304
- 售价：35.6

内容大纲
作者Halmos在遍历理论、代数逻辑、算子理论等方面的研究很有成就。本书是Springer《数学研究生教材》丛书之１８卷，是测度论的经典名著，书中对测度论作了较全面的论述，并详细介绍了前苏联和法国各学派的研究工作及其重要成果。目次：集合与类；测度和外测度；测度的扩张；测度函数；积分；一般集合函数；积空间；变换和函数；概率；局部紧空间；Huar测度；群中的测度和拓扑。读者对象：数学专业的研究生及科研人员。
作者介绍
目录
Preface
Acknowledgments
0. Prerequisites
CHAPTER Ⅰ:SETS AND CLASSES
  1.Set inclusion
  2.Unions and intersections
  3.Limits, complements, and differences
  4.Rings and algebras
  5.Generated rings and σ-rings
  6.Monotone classes
CHAPTER Ⅱ:MEASURES AND OUTER MEASURES
  7.Measure on rings
  8.Measure on intervals
  9.Properties of measures
  10.Outer measures
  11.Measurable sets
CHAPTER Ⅲ:EXTENSION OF MEASURES
  12.Properties of induced measures
  13.Extension, completion, and approximation
  14.Inner measures
  15.Lebesgue measure
  16.Non measurable sets
CHAPTER Ⅳ:MEASUKABLE FUNCTIONS
  17.Measure spaces
  18.Measurable functions
  19.Combinations of measurable functions
  20.Sequences of measurable functions
  21.Pointwise convergence
  22.Convergence in measure
CHAPTER Ⅴ:INTEGRATION
  23.Integrable simple functions
  24.Sequences of integrablc simple functions
  25.Integrable Functions
  26.Sequences of intcgrablc functions
  27.Properties of integrals
CHAPTER Ⅵ:GENERAL SET FUNCTIONS
  28.Signed measures
  29.Hahn and Jordan decompositions
  30.Absolute continuity
  31.The Radon-Nikodym theorem
  32.Derivatives of signed measures
CHAPTER Ⅶ:PRODUCT SPACES
  33.Cartesian products
  34.Sections
  35.Product measures
  36.Fubini's theorem
  37.Finite dimensional product spaces
  38.Infinitc dimensional product spaces
CHAPTER Ⅷ:TRANSFORMATIONS AND FUNCTIONS
  39.Measurable transformations

  40.Measure rings
  41.The isomorphism theorem
  42.Function spaces
  43.Set functions and point functions
CHAPTER Ⅸ:PROBABILITY
  44.Heuristic introduction
  45.Independence
  45.Series of independent functions
  47.The law of large numbers
  48.Conditional probabilities and expectations
  49.Measures on product spaces
CHAPTER Ⅹ: LOCALLY COMPACT SPACES
  50.Topological lemmas
  51.Borel sets and Baire sets
  52.Regular measures
  53.Generation of Borel measures
  54.Regular contents
  55.Classes of continuous functions
  56.Linear functionals
CHAPTER Ⅺ: HAAR MEASURE
  57.Full subgroups
  58.Existence
  59.Measurable groups
  60.Uniqueness
CHAPTER Ⅻ: MEASURE AND TOPOLOGY IN GROUPS
  61.Topology in terms of measure
  62.Weil topology
  63.Quotient groups
  64.The regularity of Haar measure
References
Bibliography
List of frequently used symbols
Index

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