Kechris, Alexander S.
Topics in Orbit Equivalence [electronic resource] / by Alexander S. Kechris. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. - X, 138 p. online resource. - Lecture Notes in Mathematics, 1852 1617-9692 ; . - Lecture Notes in Mathematics, 1852 .
Preface -- I. Orbit Equivalence -- II. Amenability and Hyperfiniteness -- III. Costs of Equivalence Relations and Groups -- References -- Index.
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.
9783540445081
10.1007/b99421 doi
Mathematics.
Harmonic analysis.
Differentiable dynamical systems.
Logic, Symbolic and mathematical.
Topology.
Mathematics.
Mathematical Logic and Foundations.
Real Functions.
Dynamical Systems and Ergodic Theory.
Abstract Harmonic Analysis.
Topology.
QA8.9-10.3
511.3
Topics in Orbit Equivalence [electronic resource] / by Alexander S. Kechris. - Berlin, Heidelberg : Springer Berlin Heidelberg, 2004. - X, 138 p. online resource. - Lecture Notes in Mathematics, 1852 1617-9692 ; . - Lecture Notes in Mathematics, 1852 .
Preface -- I. Orbit Equivalence -- II. Amenability and Hyperfiniteness -- III. Costs of Equivalence Relations and Groups -- References -- Index.
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.
9783540445081
10.1007/b99421 doi
Mathematics.
Harmonic analysis.
Differentiable dynamical systems.
Logic, Symbolic and mathematical.
Topology.
Mathematics.
Mathematical Logic and Foundations.
Real Functions.
Dynamical Systems and Ergodic Theory.
Abstract Harmonic Analysis.
Topology.
QA8.9-10.3
511.3