Amenable actions and almost invariant sets |
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| Authors: | Alexander S Kechris Todor Tsankov |
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| Institution: | Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125 ; Department of Mathematics 253-37, California Institute of Technology, Pasadena, California 91125 |
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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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| Keywords: | Generalized Bernoulli shifts amenable actions almost invariant sets $E_0$-ergodicity |
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