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 …

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 …

1. Introduction. In this paper we announce the introduction of a new notion of amenability for
ergodic group actions and ergodic equivalence relations. Amenable ergodic actions occupy …

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 …

1. Introduction. Throughout,(X, B) will be a standard Borel space, G some countable group of
automorphisms, RG the equivalence relation {(x, g• x), g GG}, and fi a a-finite measure on X …

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 …

1. Introduction. Throughout this paper the term'probability space'will denote a nonatomic
Lebesgue probability space. Let G be a countable group,(X, 8, It) a probability space, and let …

Let $(X,\mathcal {B}) $ be a standard Borel space, $ R\subset X\times X $ an equivalence
relation $\in\mathcal {B}\times\mathcal {B} $. Assume each equivalence class is countable …

On the von Neumann Algebra of an Ergodic Group Action Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 66, Number 2, October 1977 ON THE VON …

As with unitary representations, one can induce an ergodic action of a closed subgroup of a
locally compact group G to obtain an ergodic action of G. We show that every amenable …