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 …

The theory of definable equivalence relations has been a very active area of research in
descriptive set theory during the last three decades. It serves as a foundation of a theory of …

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 …

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 present some recent rigidity results for von Neumann algebras (II1 factors) and
equivalence relations arising from measure preserving actions of groups on probability …

We study the analogue, in orbit equivalence, of free product decompositions and free
indecomposability for countable groups. We introduce the (orbit equivalence invariant) …

A long-standing open problem in the theory of hyperfinite equivalence relations asks
whether the orbit equivalence relation generated by a Borel action of a countable amenable …

We replace measure with category in an argument of GW Mackey to characterize closed
subgroups H of a totally nonmeager, 2nd countable topological group G in terms of the …

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 …

It has been shown by J. Feldman, P. Hahn and CC Moore that every non-singular action of a
second countable locally compact group has a countable (in fact so-called lacunary) …