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Finite uniform generators for ergodic, finite entropy, free actions of amenable groups
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  • Published: February 1988

Finite uniform generators for ergodic, finite entropy, free actions of amenable groups

  • A. Rosenthal1,2 

Probability Theory and Related Fields volume 77, pages 147–166 (1988)Cite this article

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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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Authors and Affiliations

  1. Laboratoire de Probabilités, Université de Paris 6, Tour 56 3eme Étage, 4 Place Jussieu, F-75230, Paris Cedex 05, France

    A. Rosenthal

  2. Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem, Israel

    A. Rosenthal

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  1. A. Rosenthal
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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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  • Received: 01 September 1986

  • Issue Date: February 1988

  • DOI: https://doi.org/10.1007/BF00334034

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Keywords

  • Entropy
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Lebesgue Space
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