Lectures on ergodic theory(遍历理论讲稿)

2006-4  

AMS  

Halmos  

99  

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.

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

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