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 …

Amenable Actions of Groups Page 1 TRANSACTIONS OF THE AMERICAN MATHEMATICAL
SOCIETY Volume 344, Number 2, August 1994 AMENABLE ACTIONS OF GROUPS SCOT …

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 …

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 …

This book is based on a course given at the University of Chicago in 1980-81. As with the
course, the main motivation of this work is to present an accessible treatment, assuming …

In this paper we shall study extensions in the theory of ergodic actions ofa locally compact
group. If G isa locally compact group, by an ergodic G-space we mean a Lebesgue space …

Ergodic theory in its broadest sense is the study of group actions on measure spaces.
Historically the discipline has tended to concentrate on the framework of integer actions, in …

We will be dealing with actions of groups on Lebesgue spaces. That is, given a locally
compact group G and a Lebesgue space (X, A, m), a G-action is a measurable mapping G x …

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 …