Geodesic
Ergodic actions of countable groups and finite generating partitions
Brandon Seward1
1Hebrew University, Jerusalem, Israel
Groups, geometry, and dynamics, Tome 9 (2015) no. 3, pp. 793-810

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DOI

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.
DOI : 10.4171/ggd/328
Classification : 37-XX
Mots-clés : Finite generator, generating partition, Shannon entropy, Krieger’s finite generator theorem, ergodic, countable groups, f-invariant, sofic

Brandon Seward  1

1 Hebrew University, Jerusalem, Israel 
Brandon Seward. Ergodic actions of countable groups and finite generating partitions. Groups, geometry, and dynamics, Tome 9 (2015) no. 3, pp. 793-810. doi: 10.4171/ggd/328
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     title = {Ergodic actions of countable groups and finite generating partitions},
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     year = {2015},
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     number = {3},
     doi = {10.4171/ggd/328},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/328/}
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