Actions of Locally Compact Groups

Manfred Einsiedler () and Thomas Ward ()
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Manfred Einsiedler: ETH Zurich, Departement Mathematik
Thomas Ward: University of East Anglia, School of Mathematics

Chapter Chapter 8 in Ergodic Theory, 2011, pp 231-275 from Springer

Abstract: Abstract 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.

Keywords: Invariant Measure; Compact Group; Haar Measure; Ergodic Theorem; Amenable Group (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-85729-021-2_8

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DOI: 10.1007/978-0-85729-021-2_8

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