This paper is motivated by an old and central problem in measurable dynamics: given two dynamical systems, determine whether or not they are measurably conjugate, i.e., isomorphic. Let us set some notation. A dynamical system (or system for short) is a triple (G,X, μ), where (X,μ) is a probability space and G is a group acting by measure-preserving transformations on (X,μ). We will also call this a dynamical system over G, a G-system or an action of G. In this paper, G will always be a discrete… CONTINUE READING