Topics in Orbit Equivalence

  • Authors
  • Alexander S. Kechris

Part of the Lecture Notes in Mathematics book series (LNM, volume 1852)

Table of contents

  1. Front Matter
    Pages N2-X
  2. Alexander S. Kechris, Benjamin D. Miller
    Pages 1-6
  3. Alexander S. Kechris, Benjamin D. Miller
    Pages 7-53
  4. Alexander S. Kechris, Benjamin D. Miller
    Pages 55-128
  5. Alexander S. Kechris, Benjamin D. Miller
    Pages 129-130
  6. Alexander S. Kechris, Benjamin D. Miller
    Pages 131-134
  7. Back Matter
    Pages 129-135

About this book

Introduction

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 amenability. Included here are proofs of Dye's theorem that probability measure-preserving, ergodic actions of the integers are orbit equivalent and of the theorem of Connes-Feldman-Weiss identifying amenability and hyperfiniteness for non-singular equivalence relations. The presentation here is often influenced by descriptive set theory, and Borel and generic analogs of various results are discussed. The final chapter is a detailed account of Gaboriau's recent results on the theory of costs for equivalence relations and groups and its applications to proving rigidity theorems for actions of free groups.

Keywords

Equivalence amenability cost equivalence relations hyperfiniteness orbit equivalence set set theory

Bibliographic information

  • DOI https://doi.org/10.1007/b99421
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-22603-1
  • Online ISBN 978-3-540-44508-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book