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Amenable Actions and Almost Invariant Sets

Alexander S. Kechris and Todor Tsankov
Proceedings of the American Mathematical Society
Vol. 136, No. 2 (Feb., 2008), pp. 687-697
Stable URL: http://www.jstor.org/stable/20535137
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Amenable Actions and Almost Invariant Sets
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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 $M^{X}$, where M is a measure space. In particular, we show that the action of Γ on X is amenable iff the shift $\Gamma \curvearrowright M^{X}$ has almost invariant sets.

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