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Topics in Orbit Equivalence / Edition 1
     

Topics in Orbit Equivalence / Edition 1

by Alexander Kechris
 

ISBN-10: 3540226036

ISBN-13: 9783540226031

Pub. Date: 10/15/2004

Publisher: Springer Berlin Heidelberg

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

Overview

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

ISBN-13:
9783540226031
Publisher:
Springer Berlin Heidelberg
Publication date:
10/15/2004
Series:
Lecture Notes in Mathematics Series , #1852
Edition description:
2004
Pages:
138
Product dimensions:
0.32(w) x 6.14(h) x 9.21(d)

Table of Contents

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

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