Topics in Orbit Equivalence: 1852 (Lecture Notes in Mathematics, 1852) - Softcover

Kechris, Alexander; Miller, Benjamin D.

 
9783540226031: Topics in Orbit Equivalence: 1852 (Lecture Notes in Mathematics, 1852)
Softcover
ISBN 10: 3540226036 ISBN 13: 9783540226031
Publisher: Springer, 2004

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2004
Language
English
ISBN 10 
3540226036
ISBN 13 
9783540226031
Binding
Paperback
Number of pages
148