Ergodic actions of countable groups and finite generating partitions

2012/06/26 by Seward, Brandon
#37A15 (Primary) 37A35 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1206.6005

Abstract

We prove that if an ergodic action of a countable group on a probability space admits a generating partition having finite Shannon entropy then it admits a finite generating partition.

Related

• Krieger's finite generator theorem for actions of countable groups I
• Krieger's finite generator theorem for actions of countable groups II
• Kac's Lemma and countable generators for actions of countable groups
• Krieger's finite generator theorem for actions of countable groups III
• Finite generators for countable group actions in the Borel and Baire\n category settings