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Amenable actions and almost invariant sets
Author(s):
Alexander
S.
Kechris;
Todor
Tsankov
Journal:
Proc. Amer. Math. Soc.
136
(2008),
687-697.
MSC (2000):
Primary 28D15;
Secondary 43A07
Posted:
November 3, 2007
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Abstract:
In this paper, we study the connections between properties of the action of a countable group  on a countable set  and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of  on  , where  is a measure space. In particular, we show that the action of  on  is amenable iff the shift  has almost invariant sets.
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Additional Information:
Alexander
S.
Kechris
Affiliation:
Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
Email:
kechris@caltech.edu
Todor
Tsankov
Affiliation:
Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125
Email:
todor@caltech.edu
DOI:
10.1090/S0002-9939-07-09116-2
PII:
S 0002-9939(07)09116-2
Keywords:
Generalized Bernoulli shifts,
amenable actions,
almost invariant sets,
$E_0$-ergodicity
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
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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