Topics in Orbit Equivalence (Lecture Notes in Mathematics, 1852)

Kechris, Alexander,Miller, Benjamin D.

ISBN 10: 3540226036 / ISBN 13: 9783540226031

Published by Springer, 2004

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Bibliographic Details

• Title: Topics in Orbit Equivalence (Lecture Notes in Mathematics, 1852)
• Publisher: Springer
• Publication Date: 2004
• Language: English
• ISBN 10: 3540226036
• ISBN 13: 9783540226031
• Binding: paperback
• Condition: Good

About this title

Synopsis

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.