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Amenable actions and almost invariant sets

Kechris, Alexander S. and Tsankov, Todor (2008) Amenable actions and almost invariant sets. Proceedings of the American Mathematical Society, 136 (2). pp. 687-697. ISSN 0002-9939. doi:10.1090/S0002-9939-07-09116-2.

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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 Γ → M^X has almost invariant sets.

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Additional Information:© 2007 American Mathematical Society. Received by editor(s): October 2, 2006. Received by editor(s) in revised form: February 8, 2007. Posted: November 3, 2007. Additional Notes: This research was partially supported by NSF grant DMS-0455285. Communicated by: Jane M. Hawkins.
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Subject Keywords:generalized Bernoulli shifts; amenable actions; almost invariant sets; E-0-ergodicity
Issue or Number:2
Record Number:CaltechAUTHORS:KECpams08
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Official Citation:Must include set publisher statement - (First published in [Publication] in [volume and number, or year], published by the American Mathematical Society)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13824
Deposited By: Tony Diaz
Deposited On:02 Apr 2009 19:06
Last Modified:08 Nov 2021 22:40

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