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Lectures on Ergodic Theory
Paul Halmos, Santa Clara University, CA

AMS Chelsea Publishing
1956; 99 pp; hardcover
Volume: 142
ISBN-10: 0-8218-4125-4
ISBN-13: 978-0-8218-4125-9
List Price: US$28
Member Price: US$25.20
Order Code: CHEL/142.H
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See also:

Ergodic Theory, Groups, and Geometry - Robert J Zimmer and Dave Witte Morris

This classic book is based on lectures given by the author at the University of Chicago in 1956. The topics covered include, in particular, recurrence, the ergodic theorems, and a general discussion of ergodicity and mixing properties. There is also a general discussion of the relation between conjugacy and equivalence. With minimal prerequisites of some analysis and measure theory, this work can be used for a one-semester course in ergodic theory or for self-study.


Graduate students and research mathematicians interested in number theory.

Table of Contents

  • Introduction
  • Examples
  • Recurrence
  • Mean convergence
  • Pointwise convergence
  • Comments on the ergodic theorem
  • Ergodicity
  • Consequences of ergodicity
  • Mixing
  • Measure algebras
  • Discrete spectrum
  • Automorphisms of compact groups
  • Generalized proper values
  • Weak topology
  • Weak approximation
  • Uniform topology
  • Uniform approximation
  • Category
  • Invariant measures
  • Invariant measures: the solution
  • Invariant measures: the problem
  • Generalized ergodic theorems
  • Unsolved problems
  • References
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