Groups, Geometry, and Dynamics


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Volume 9, Issue 3, 2015, pp. 793–810
DOI: 10.4171/GGD/328

Published online: 2015-10-29

Ergodic actions of countable groups and finite generating partitions

Brandon Seward[1]

(1) Hebrew University, Jerusalem, Israel

We prove the following finite generator theorem. Let $G$ be a countable group acting ergodically on a standard probability space. Suppose this action admits a generating partition having finite Shannon entropy. Then the action admits a finite generating partition. We also discuss relationships between generating partitions and f-invariant and sofic entropies.

Keywords: Finite generator, generating partition, Shannon entropy, Krieger’s finite generator theorem, ergodic, countable groups, f-invariant, sofic

Seward Brandon: Ergodic actions of countable groups and finite generating partitions. Groups Geom. Dyn. 9 (2015), 793-810. doi: 10.4171/GGD/328