We consider a countable discrete group $\Gamma $ acting ergodically on a standard Borel
space S with quasi-invariant measure $\mu $. Let $\pi $ be a unitary representation of …

A group $ G $ acts on a set $ X $, and $\mu $ is a $ G $-invariant measure on $ X $. Under
certain assumptions on the action of $ G $ and on $\mu $(eg, $ G $ acts freely and is …

If a countable discrete group acts ergodically on a standard Borel space with a quasi-
invariant measure, there is a von Neumann algebra associated to it by the classical …

We show that a measured G-space (X, μ), where G is a locally compact group, is amenable
in the sense of Zimmer if and only if the following two conditions are satisfied: the associated …

Let X be a compact metrizable space,~(X) its G-algebra of Borel sets, and let T be a
homeomorphism of X. We denote for a Borel measure# on X by T/2 the measure that is …

Classical ergodic theory deals with measure (or measure class) preserving actions of locally
compact groups on Lebesgue spaces. An important tool in this setting is a theorem of …

Let G be a locally compact second countable group, and let (g, x)→ gx be a properly ergodic
nonsingular action of G on a probability space (X, I, μ). This action is called mildly mixing if …

Let $ G $ be an amenable discrete countable infinite group, let $ A $ be a finite set, and let
$(\mu _g) _ {g\in G} $ be a family of probability measures on $ A $ such that $\inf _ {g\in …

In this paper, we study the connections between properties of the action of a countable
group $\Gamma $ on a countable set $ X $ and the ergodic theoretic properties of the …

In 1978, RJ Zimmer introduced the notion of amenability for an action of a separable locally
compact group, or an equivalence relation, on a standard Borel space with a probability …