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 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 …

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 …

" The subject of this book is the study of ergodic, measure preserving actions of countable
discrete groups on standard probability spaces. It explores a direction that emphasizes a …

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 …

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 this paper we discuss the use of dynamical and ergodic-theoretic ideas and methods to
solve some long-standing problems originating from Lie groups and number theory. These …

Sharp ergodic theorems for group actions and strong ergodicity Page 1 Ergod. Th. & Dynam.
Sys. (1999), 19, 1037–1061 Printed in the United Kingdom c 1999 Cambridge University …

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 …

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 …