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 …

Let (~ be a separable locally compact group. Continuing the convention adopted in our
papers [11] and [12] we shall abbreviate the term" continuous unitary representation 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 …

Preliminary definitions regarding Borel groupoids are given in? 1. In? 2 we define
cohomology groups and induced homomorphisms for Borel groupoids. This is seen to be a …

The present notes arose from a series of lectures, which I gave at the School of Algebrg'in
S~ o Paulo, July 12 to July 5o,] 976. At the same time Irving Reiner has given lectures on …

There are many constructions which give rise to the hyperfinite IIX factor 51 of Murray and
von Neumann [12]. For example:(i) the infinite tensor product of a countable number of …

In the theory of representations of a finite group by linear transformations the closely related
notions of" imprimitivity" and of" induced representation" play a prominent role. In [18] the …

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 …