English

A survey of Measured Group Theory

Dynamical Systems 2010-08-10 v2 Group Theory

Abstract

The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments focused on the notion of Measure Equivalence between groups, and Orbit Equivalence between group actions. We discuss known invariants and classification results (rigidity) in both areas.

Keywords

Cite

@article{arxiv.0901.0678,
  title  = {A survey of Measured Group Theory},
  author = {Alex Furman},
  journal= {arXiv preprint arXiv:0901.0678},
  year   = {2010}
}

Comments

A survey for the Proceedings of a Conference honoring Robert Zimmer's 60th birthday. 61 pages. Referees comments are incorporated, in particular sections 3.1.2 (cost) and 3.1.4 (Cowling Haagerup invariant) were updated. Some new references added

R2 v1 2026-06-21T11:58:00.078Z