Amenable Actions and Almost Invariant Sets

Abstract

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

Cite this paper

@inproceedings{Kechris2006AmenableAA, title={Amenable Actions and Almost Invariant Sets}, author={Alexander S. Kechris and Todor Tsankov}, year={2006} }