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arXiv · 1210.1992

Entropy theory for sofic groupoids I: the foundations

Lewis Bowen
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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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Lewis Bowen. 2012-10-06. Entropy theory for sofic groupoids I: the foundations. https://arxiv.org/abs/1210.1992

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