ABSTRACT A countable group F has property T of Kazhdan if and only if no measure
preserving ergodic action of F has non-trivial asymptotically invariant sets. A countable …

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 …

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 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 …

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 …

272 PETER FORREST abstract generalization of Warren Ambrose's theorem. Not much
more can be said in this general case (see Proposition 6.3). However, if C contains an …

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 …

§ 0. Introduction. Let (X, M, X) be a finite or «--finite measure space. For the group M of
invertible, measure preserving transformations, or more ge ally for the group'S of invertible …

For any countable group T satisfying the “weak Rohlin property”, and for each dynamical
property, the set of T-actions with that property is either residual or meager. The class of …

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 …