Finite uniform generators for ergodic, finite entropy, free actions of amenable groups
type: Item
instance of: scholarly article
title: Finite uniform generators for ergodic, finite entropy, free actions of amenable groups
zbMATH Open document ID: 0614.28017
DOI: 10.1007/BF00334034
author: Yanyan Li
publication date: 1988-01-01T00:00:00Z
review text: Let (X,\({\mathcal B},\mu)\) be a Lebesgue space. We prove in the first part of this paper that any ergodic \({\mathbb{Z}}^ 2\)-action on \((X,{\mathcal B},\mu)\) with finite entropy \(h<Log k\) has generating partition T that is uniform and has k atoms. In the second part, we prove a similar result for any ergodic, free G-action with finite entropy \(h<Log (k-2),\) for any discrete amenable group G.
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 28D15
zbMATH DE Number: 3993911
zbMATH Keywords: Lebesgue space
zbMATH Keywords: ergodic \({\mathbb Z}^ 2\)-action
zbMATH Keywords: finite entropy
zbMATH Keywords: free G- action
zbMATH Keywords: discrete amenable group
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3993911