Finite uniform generators for ergodic, finite entropy, free actions of amenable groups (Q1820267)

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.