On a theorem Dan Rudolph: Part II: Amenable groups

Abstract

We prove an analog of Rudolph's theorem for actions of countable amenable groups, which asserts that among invariant measures with entropy at least c on the $G$-shift $(\hat{I}{›}^G,\ddot{I}ƒ)$, a typical measure has entropy $c$ and is Bernoulli. We also address a relative version of this theorem.

16 pages, 1 figure