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Invariant Measures
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1999; 134 pp; softcover
Reprint/Revision History:
reprinted 2000
ISBN-10: 0-8218-0912-1
ISBN-13: 978-0-8218-0912-9
List Price: US$45 Member Price: US$36
Order Code: INMEAS

In 1940-1941 von Neumann lectured on invariant measures at the Institute for Advanced Study at Princeton. This book is essentially a written version of those lectures.

The lectures began with general measure theory and went on to Haar measure and some of its generalizations. Shizuo Kakutani was at the Institute that year, and he and von Neumann had many conversations on the subject. The conversations revealed facts and produced proofs. Quite a bit of the content of the course, especially toward the end, was discovered a few weeks before it appeared on the blackboard. The original version of these notes was prepared by Paul Halmos, von Neumann's assistant that year. Von Neumann read the handwritten version before it went to the typist and sometimes scribbled comments on the margins; he rewrote most of Chapter 6. This book is the first published version of the original notes.

Graduate students and research mathematicians working in classical measure theory and analysis on general topological groups.

Reviews

"The present American Mathematical Society publication essentially represents a collection of lectures given by von Neumann at the Institute for Advanced Study during 1940-41. Although the material is foundational, important, and is the basis for various graduate texts, it serves the purpose of both history and usefulness to have it available under one cover."

-- Zentralblatt MATH

• Measure theory
• Generalized limits
• Haar measure
• Uniqueness
• Measure and topology
• Construction of Haar's invariant measure in groups by approximately equidistributed finite point sets and explicit evaluations of approximations