The joys of Haar measure
著者
書誌事項
The joys of Haar measure
（Graduate studies in mathematics, v. 150）
American Mathematical Society, c2014
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注記
Includes bibliographical references (p. 309-315) and indexes
内容説明・目次
内容説明
From the earliest days of measure theory, invariant measures have held the interests of geometers and analysts alike, with the Haar measure playing an especially delightful role. The aim of this book is to present invariant measures on topological groups, progressing from special cases to the more general. Presenting existence proofs in special cases, such as compact metrizable groups, highlights how the added assumptions give insight into just what the Haar measure is like; tools from different aspects of analysis and/or combinatorics demonstrate the diverse views afforded the subject.
After presenting the compact case, applications indicate how these tools can find use. The generalisation to locally compact groups is then presented and applied to show relations between metric and measure theoretic invariance. Steinlage's approach to the general problem of homogeneous action in the locally compact setting shows how Banach's approach and that of Cartan and Weil can be unified with good effect. Finally, the situation of a nonlocally compact Polish group is discussed briefly with the surprisingly unsettling consequences indicated.
The book is accessible to graduate and advanced undergraduate students who have been exposed to a basic course in real variables, although the authors do review the development of the Lebesgue measure. It will be a stimulating reference for students and professors who use the Haar measure in their studies and research.
目次
Preface
Lebesgue measure in Euclidean space
Measures on metric spaces
Introduction to topological groups
Banach and measure
Compact groups have a Haar measure
Applications
Haar measure on locally compact groups
Metric invariance and Haar measure
Steinlage on Haar measure
Oxtoby's view of Haar measure
Appendix A
Appendix B
Bibliography
Author index
Subject index
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