Let G and H be infinite finitely generated amenable groups. This paper studies two notions
of equivalence between actions of such groups on standard Borel probability spaces. They …

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 …

In [R1] a notion of restricted orbit equivalence for ergodic transformations was developed.
Here we modify that structure in order to generalize it to actions of higher-dimensional …

We give a brief survey of some classification results on orbit equivalence of probability
measure preserving actions of countable groups. The notion of ℓ 2 Betti numbers for groups …

Inspired by [17], we develop an orbital approach to the entropy theory for actions of
countable amenable groups. This is applied to extend–with new short proofs–the recent …

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 …

We consider several weaker versions of the notion of conjugacy and orbit equivalence of
measure preserving actions of countable groups on probability spaces, involving …

Previous work introduced two measure-conjugacy invariants: the f-invariant (for actions of
free groups) and Σ-entropy (for actions of sofic groups). The purpose of this paper is to show …

The overarching theme of this thesis is the study of orbit equivalence as an equivalence
relation in the context of Borel reducibility. The thesis is divided in two parts: Chapter 1 is …

Let G be a non-periodic amenable group. We prove that there does not exist a topological
action of G for which the set of ergodic invariant measures coincides with the set of all …