Ergodic actions of countable groups and finite generating partitions
Brandon SewardHebrew University, Jerusalem, Israel
We prove the following finite generator theorem. Let 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.
Cite this article
Brandon Seward, Ergodic actions of countable groups and finite generating partitions. Groups Geom. Dyn. 9 (2015), no. 3, pp. 793–810DOI 10.4171/GGD/328