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Amenable equivalence relations and the construction of ergodic averages for group actions

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Abstract

We present a general new method for constructing pointwise ergodic sequences on countable groups which is applicable to amenable as well as to non-amenable groups and treats both cases on an equal footing. The principle underlying the method is that both cases can be viewed as instances of the general ergodic theory of amenable equivalence relations.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Texas, Austin, TX, 78712-0257, USA

    Lewis Bowen

  2. Department of Mathematics, Technion — Israel Institute of Technology, Haifa, 32000, Israel

    Amos Nevo

Authors
  1. Lewis Bowen
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  2. Amos Nevo
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Correspondence to Lewis Bowen.

Additional information

supported in part by NSF grant DMS-0968762, NSF CAREER Award DMS-0954606, and BSF grant 2008274

supported in part ISF grant and BSF grant 2008274

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Bowen, L., Nevo, A. Amenable equivalence relations and the construction of ergodic averages for group actions. JAMA 126, 359–388 (2015). https://doi.org/10.1007/s11854-015-0021-5

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  • DOI: https://doi.org/10.1007/s11854-015-0021-5

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