The basic properties of measure-preserving actions of more general groups are described. Two important examples of actions generated by commuting group automorphisms are introduced, and their mixing properties described. Some of the basic machinery of the ergodic theory of groups actions is developed: Haar measures, regular representations, amenability, mean ergodic theorems and the ergodic decomposition. The pointwise ergodic theorem is proved for a class of groups with polynomial growth, developing the approach to the maximal theorem via a covering lemma from Chapter 2.
KeywordsInvariant Measure Compact Group Haar Measure Ergodic Theorem Amenable Group
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