The basic idea in using group representations for questions of ergodicity is the following. If G
acts ergodically on (S, p), where p is a finite G-invariant measure, then there is a naturally …

An important problem in ergodic theory is to determine when the restriction to a subgroup of
an ergodic action of a group is still ergodic. Classical results concerning the ergodicity of …

1. Introduction.-In this note we shall show how two programs announced earlier may be
extended and partially unified by means of the concept of an" ergodic groupoid." The first of …

Let G be a connected Lie group, and let C and D be lattices in G, that is, discrete subgroups
such that the homogeneous spaces G/C and G/D have fmite G-invariant measures. Let C act …

Suppose F is a discrete group and (S, yt) is a finite measure space on which F acts so that [i
is invariant and ergodic. If F is amenable, it follows from results of [4],[3] that the F-action is …

1.1. Measurable actions. Let us begin by recalling some well-known facts which are needed
in order to establish the existence of the operators which are the subject of the present …

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 …

These notes are divided into two rather distinct parts, the first of which concerns the
restriction of unitary representations of a group to one of its subgroups, and the connection …

1. Introduction. The point of this paper is to study the low dimensional cohomology theory of
ergodic actions of semisimple Lie groups and their lattice subgroups. The rigidity theorem for …

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 …