Lectures on Ergodic Theory

This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented."
Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.

Hungarian-born Paul R. Halmos (1916–2006) is widely regarded as a top-notch expositor of mathematics. He taught at the University of Chicago and the University of Michigan as well as other universities and made significant contributions to several areas of mathematics including mathematical logic, probability theory, ergodic theory, and functional analysis.

IntroductionExamplesRecurrenceMean convergencePointwise convergenceComments on the ergodic theoremMixingMeasure algebrasDiscrete spectrumAutomorphisms of compact groupsGeneralized proper valuesWeak topologyWeak approximationUniform topologyUniform approximationCategoryInvariant measuresInvariant measures: the solutionInvariant measures: the problemGeneralized ergodic theoremsUnsolved problemsReferences