All Questions

Suppose we have a discrete group $G$ acting on a compact set $X \subseteq \mathbb{R}^d$ via measure-preserving homeomorphisms, and suppose we have a point $x$ whose orbit $Gx$ is finite (say $|Gx| = n$...

Let $G$ be a finitely generated group. The amenability of $G$ is equivalent to the existence of a certain "weak measure" on $G$. Is there such a characterization for residually amenable groups as well?...