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 …

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 …

The main result of Part I is Theorem 1. This is a maximal theorem for certain operators on
abstract L spaces, where 1? p< oo and E is a Banach space. This theorem contains as …

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 …

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 POINTWISE ERGODIC THEOREM FOR AMENABLE GROUPS. 473 among other
things, that the appropriate ergodic averages always converge in norm to a G-invariant …

A question naturally arising in dynamical systems is: does a flow {~ t} have the same
nonwandering set as most of the time t maps, ç) This and similar questions for recurrency …

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 …

The aim of this paper is to prove an analogue of the strong rigidity theorems for lattices in
semisimple Lie groups of Mostow and Margulis in the context of ergodic actions of …

Ergodic theorems and the construction of summing sequences in amenable locally compact
groups Page 1 COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, VOL. XXVI …