All Questions

In "Countable sections for locally compact group actions" (Ergod. Th. & Dynam. Sys., 1992), Kechris proved that if $G$ is a Polish locally compact group acting in a Borel way on a ...

In attempting to understand the paper "Superrigidity, Weyl groups, and actions on the circle" of Uri Bader, Alex Furman and Ali Shaker (linked at Furman's page) I find that towards the end of the ...

Let $G$ be a finitely-generated group of polynomial growth equipped with the word metric (with respect to a fixed symmetric generating set). Let \begin{equation*} A = \left\{ g \in G: |g| = mn, n \...

Let $\mathbb{G}$ be a discrete amenable semigroup, and $\left\{ F_{n}\right\} $ a Folner sequence. For $S\subset \mathbb{G}$ define the upper density as $D^{\ast }(S)=\limsup_{n\rightarrow \infty }\...

As everyone knows if $x\in S^1$, then the set $\{ x^n \}$ is either finite or dense. Under which condition is true for any other locally compact group, i.e if $G$ is a locally compact group, and $x\in ...