This volume provides a self-contained introduction to some topics in orbit equivalence
theory, a branch of ergodic theory. The first two chapters focus on hyperfiniteness and …

Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility,
and measures preserving group actions considered up to orbit equivalence. This title …

For Γ a countable amenable group consider those actions of Γ as measure-preserving
transformations of a standard probability space, written as {Tγ} γ∈ Γ acting on (X, F, μ). We …

arXiv:1009.0132v1 [math.GR] 1 Sep 2010 Page 1 arXiv:1009.0132v1 [math.GR] 1 Sep 2010
Orbit Equivalence and Measured Group Theory Damien Gaboriau∗ May, 2010 Abstract We …

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 …

Consider a countable group Γ acting ergodically by measure preserving transformations on
a probability space (X, μ), and let RΓ be the corresponding orbit equivalence relation on X …

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 …

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 …

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 …

Ergodic theory in its broadest sense is the study of group actions on measure spaces.
Historically the discipline has tended to concentrate on the framework of integer actions, in …