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 …

In a recent note [ti] the author has given a highly condensed and largely unmotivated
account of the basic notions in a theory whose aim is to bring to light and exploit certain …

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 …

Let the real line act ergodically on the finite measure space S, so as to preserve the
measure. Form the Hilbert space 22 (S,) and for each real x let U be the unitary …

Many mathematicians are aware of some of the dramatic interactions between ergodic
theory and other parts of the subject, notably Ramsey theory, infinite combinatorics, and …

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 …

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 …

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 …

A fundamental problem in geometry is to understand the automorphism group of a geometric
structure. In this paper, we discuss the contribution that ergodic theory can make in this …