Topics in Orbit Equivalence |
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Author:
| Kechris, Alexander S. Miller, Benjamin D. |
Series title: | Lecture Notes in Mathematics Ser. |
ISBN: | 978-3-540-22603-1 |
Publication Date: | Aug 2004 |
Publisher: | Springer Berlin / Heidelberg
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Imprint: | Springer |
Book Format: | Paperback |
List Price: | USD $49.95USD $44.99 |
Book Description:
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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...
More DescriptionThis 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.