Haar 测度的乐趣（影印版）

样章

作者：

Joe Diestel, Angela Spalsbury

定价：

135.00 元

版面字数：

540千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-063247-7

物料号：

63247-00

出版时间：

2025-02-14

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

分析

暂无

目录
- 前辅文
- Preface
- Chapter 1. Lebesgue Measure in Euclidean Space
  - §1. An Introduction to Lebesgue Measure
  - §2. The Brunn–Minkowski Theorem
  - §3. Covering Theorem of Vitali
  - §4. Notes and Remarks
- Chapter 2. Measures on Metric Spaces
  - §1. Generalities on Outer Measures
  - §2. Regularity
  - §3. Invariant Measures on Rn
  - §4. Notes and Remarks
- Chapter 3. Introduction to Topological Groups
  - §1. Introduction
  - §2. The Classical (Locally Compact) Groups
  - §3. The Birkhoff–Kakutani Theorem
  - §4. Products of Topological Spaces
  - §5. Notes and Remarks
- Chapter 4. Banach and Measure
  - §1. Banach Limits
  - §2. Banach and Haar Measure
  - §3. Saks’ Proof of C(Q)*, Q a Compact Metric Space
  - §4. The Lebesgue Integral on Abstract Spaces
  - §5. Notes and Remarks
- Chapter 5. Compact Groups Have a Haar Measure
  - §1. The Arzelá–Ascoli Theorem
  - §2. Existence and Uniqueness of an Invariant Mean
  - §3. The Dual of C(K)
  - §4. Notes and Remarks
- Chapter 6. Applications
  - §1. Homogeneous Spaces
  - §2. Unitary Representations: The Peter–Weyl Theorem
  - §3. Pietsch Measures
  - §4. Notes and Remarks
- Chapter 7. Haar Measure on Locally Compact Groups
  - §1. Positive Linear Functionals
  - §2. Weil’s Proof of Existence
  - §3. A Remarkable Approximation Theorem of Henri Cartan
  - §4. Cartan’s Proof of Existence of a Left Haar Integral
  - §5. Cartan’s Proof of Uniqueness
  - §6. Notes and Remarks
- Chapter 8. Metric Invariance and Haar Measure
  - §1. Notes and Remarks
- Chapter 9. Steinlage on Haar Measure
  - §1. Uniform Spaces: The Basics
  - §2. Some Miscellaneous Facts and Features about Uniform Spaces
  - §3. Compactness in Uniform Spaces
  - §4. From Contents to Outer Measures
  - §5. Existence of G-invariant Contents
  - §6. Steinlage: Uniqueness and Weak Transitivity
  - §7. Notes and Remarks
- Chapter 10. Oxtoby’s View of Haar Measure
  - §1. Invariant Measures on Polish Groups
  - §2. Notes and Remarks
- Appendix A
- Appendix B
- Bibliography
- Author Index
- Subject Index