Amenable actions and almost invariant sets
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- by Alexander S. Kechris and Todor Tsankov PDF
- Proc. Amer. Math. Soc. 136 (2008), 687-697 Request permission
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.References
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Additional Information
- Alexander S. Kechris
- Affiliation: Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 99660
- Email: kechris@caltech.edu
- Todor Tsankov
- Affiliation: Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 781832
- Email: todor@caltech.edu
- Received by editor(s): October 2, 2006
- Received by editor(s) in revised form: February 8, 2007
- Published electronically: November 3, 2007
- Additional Notes: This research was partially supported by NSF grant DMS-0455285
- Communicated by: Jane M. Hawkins
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 687-697
- MSC (2000): Primary 28D15; Secondary 43A07
- DOI: https://doi.org/10.1090/S0002-9939-07-09116-2
- MathSciNet review: 2358510