As with unitary representations, one can induce an ergodic action of a closed subgroup of a
locally compact group G to obtain an ergodic action of G. We show that every amenable …

We consider three problems concerning cocycles of ergodic group actions: behavior of
cohomology under the restriction of an ergodic semi-simple Lie group action to a lattice …

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. 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 theorems of M. Ratner, describing the finite ergodic invariant measures and the orbit
closures for unipotent flows on homogeneous spaces of Lie groups, are extended for actions …

We describe those discrete groups with finite measure preserving actions that are stably
orbit equivalent to such an action of a higher rank simple Lie group. This is applied to obtain …

Consider the following property of a topological group G: every continuous affine G-action
on a Hilbert space with a bounded orbit has a fixed point. We prove that this property …

Let U be a nilpotent, unipotent subgroup of a Lie group G, and let $\Gamma $ be a closed
subgroup of G. Marina Ratner showed that every ergodic U-invariant probability measure on …

On the von Neumann Algebra of an Ergodic Group Action Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 66, Number 2, October 1977 ON THE VON …

Let X be a compact metrizable space,~(X) its G-algebra of Borel sets, and let T be a
homeomorphism of X. We denote for a Borel measure# on X by T/2 the measure that is …