Summary
Let (Xℬμ) be a Lebesgue space. We prove in the first part of this paper that any ergodic ℤ2-action on (Xℬμ) with finite entropy hLogk has generating partition P that is uniform and has k atoms. In the second part, we prove a similar result for any ergodic, free G-action with finite entropy hLog(k-2), for any discrete amenable group G.
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Rosenthal, A. Finite uniform generators for ergodic, finite entropy, free actions of amenable groups. Probab. Th. Rel. Fields 77, 147–166 (1988). https://doi.org/10.1007/BF00334034
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DOI: https://doi.org/10.1007/BF00334034
Keywords
- Entropy
- Stochastic Process
- Probability Theory
- Statistical Theory
- Lebesgue Space