Amenable actions and almost invariant sets

Kechris, Alexander; Tsankov, Todor

doi:10.1090/S0002-9939-07-09116-2

Amenable actions and almost invariant sets
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by Alexander S. Kechris and Todor Tsankov

Proc. Amer. Math. Soc. 136 (2008), 687-697

DOI: https://doi.org/10.1090/S0002-9939-07-09116-2

Published electronically: November 3, 2007

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Abstract:

In this paper, we study the connections between properties of the action of a countable group $\Gamma$ on a countable set $X$ and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of $\Gamma$ on $M^X$, where $M$ is a measure space. In particular, we show that the action of $\Gamma$ on $X$ is amenable iff the shift $\Gamma \curvearrowright M^X$ has almost invariant sets.

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