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：

540.00千字

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

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