Approximation and Classification in the Ergodic Theory of Nonamenable Groups

Abstract

This thesis is a contribution to the theory of measurable actions of discrete groups on standard probability spaces. The focus is on nonamenable acting groups. It is organized into two parts. The first part deals with a notion called weak equivalence, which describes a sense in which such actions can approximate each other. The second part deals with the concept of entropy for measure preserving actions of sofic groups.