测度论(影印版)(英文版)
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作者(美)P.R.哈尔莫斯
出版社世界图书出版公司
ISBN9787519255848
出版时间2019-03
装帧其他
开本其他
定价89元
货号30593760
上书时间2024-06-10
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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
内容摘要
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。
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