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AuthorKechris, Alexander S. author
TitleTopics in Orbit Equivalence [electronic resource] / by Alexander S. Kechris
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2004
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Descript X, 138 p. online resource


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


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

Mathematics Mathematical analysis Analysis (Mathematics) Harmonic analysis Dynamics Ergodic theory Functions of real variables Mathematical logic Topology Mathematics Analysis Mathematical Logic and Foundations Real Functions Dynamical Systems and Ergodic Theory Abstract Harmonic Analysis Topology


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