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 …

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 …

We consider a locally compact group G with jointly continuous action G× Z→ Z on a locally
compact space. The finite Radon (regular Borel) measures M (G) act naturally on various …

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 …

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 …

This paper discusses the relations between the following properties o finite measure
preserving ergodic actions of a countable group G: strong ergodicity (ie the non-existence of …

Let G be a connected amenable group (thus, an extension of a connected normal solvable
subgroup R by a connected compact group K= GR). We show how to explicitly construct …

Let $ G $ be a countable group which is not inner amenable. Then the II $ _ {1} $-factor $ M
$ is full in the following cases:(1) $ M $ is given by the group measure space construction …

If X and Y are ergodic G-spaces, where G is a locally compact group, and X is an extension
of Y, we study a notion of amenability for the pair $(X, Y) $. This simultaneously generalizes …

Classically, ergodic theory began with the study of flows or actions of R. Later, for technical
reasons, much of the theory was first developed for actions of Z. More recently, there has …