Topics in Orbit Equivalence

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.

List of contents

Preface.
- I. Orbit Equivalence.
- II. Amenability and Hyperfiniteness.
- III. Costs of Equivalence Relations and Groups.
- References.
- Index.

Summary

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.

Product details

• Authors: Alexande Kechris, Alexander Kechris, Alexander S. Kechris, B. D. Miller, Benjamin D Miller, Benjamin D. Miller
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 28.09.2004
• EAN: 9783540226031
• ISBN: 978-3-540-22603-1
• No. of pages: 138
• Dimensions: 155 mm x 233 mm x 9 mm
• Weight: 238 g
• Illustrations: X, 138 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, B, Topologie, Dynamics, Mathematics and Statistics, Topology, Real Functions, Dynamical Systems and Ergodic Theory, Complex analysis, complex variables, Ergodic theory, Abstract Harmonic Analysis, Nonlinear science, Harmonic analysis, Dynamical systems, Functions of real variables, Mathematical logic, Mathematical Logic and Foundations, Mathematical foundations, Analysis (Mathematics), Mathematical analysis, Real analysis, real variables