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.

Readership

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