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. https://resolver.caltech.edu/CaltechAUTHORS:KECpams08
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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 Γ → M^X has almost invariant sets.
| Item Type: | Article | |||||||||
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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 | |||||||||
| DOI: | 10.1090/S0002-9939-07-09116-2 | |||||||||
| Record Number: | CaltechAUTHORS:KECpams08 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:KECpams08 | |||||||||
| 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 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 02 Apr 2009 19:06 | |||||||||
| Last Modified: | 08 Nov 2021 22:40 |
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