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Entropy theory for sofic groupoids I: The foundations

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Abstract

This is the first part in a series in which sofic entropy theory is generalized to class-bijective extensions of sofic groupoids. Here we define topological and measure entropy and prove invariance. We also establish the variational principle, compute the entropy of Bernoulli shift actions and answer a question of Benjy Weiss pertaining to the isomorphism problem for non-free Bernoulli shifts. The proofs are independent of previous literature.

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Authors and Affiliations

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

    Lewis Bowen

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  1. Lewis Bowen
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Correspondence to Lewis Bowen.

Additional information

Supported in part by NSF grant DMS-0968762 and NSF CAREER Award DMS-0954606.

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Bowen, L. Entropy theory for sofic groupoids I: The foundations. JAMA 124, 149–233 (2014). https://doi.org/10.1007/s11854-014-0030-9

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  • DOI: https://doi.org/10.1007/s11854-014-0030-9

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