Soficity, amenability, and dynamical entropy (Q2851615)

\textit{L. Bowen} [J. Am. Math. Soc. 23, No. 1, 217--245 (2010; Zbl 1201.37005)] introduced a notion of entropy for measure-preserving actions of a countable discrete sofic group. The authors used methods from operator algebras and \textit{R. Bowen}'s notion of \(\epsilon\)-separated partial orbits [Trans. Am. Math. Soc. 153, 401--414 (1971; Zbl 0212.29201)] to develop an alternative approach to this sofic entropy [Invent. Math. 186, No. 3, 501--558 (2011; Zbl 1417.37041)]. Here they show that, in the case where the acting group is amenable, the sofic measure and topological entropies coincide with their classical counterparts, independently of the sofic approximation sequence used to compute the sofic entropy. The basis for the analysis is a sofic approximation version of the Rokhlin lemma of \textit{D. S. Ornstein} and \textit{B. Weiss} [J. Anal. Math. 48, 1--141 (1987; Zbl 0637.28015)].