Topics in Orbit Equivalence
Kechris, Alexander S.
Topics in Orbit Equivalence [electronic resource] / by Alexander S. Kechris. - X, 138 p. online resource. - Lecture Notes in Mathematics, 1852 0075-8434 ; . - 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
Global analysis (Mathematics).
Logic, Symbolic and mathematical.
Mathematics.
Differentiable dynamical systems.
Harmonic analysis.
Topology.
Analysis.
Mathematical Logic and Foundations.
Real Functions.
Dynamical Systems and Ergodic Theory.
Abstract Harmonic Analysis.
Topology.
QA299.6-433
515
Topics in Orbit Equivalence [electronic resource] / by Alexander S. Kechris. - X, 138 p. online resource. - Lecture Notes in Mathematics, 1852 0075-8434 ; . - 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
Global analysis (Mathematics).
Logic, Symbolic and mathematical.
Mathematics.
Differentiable dynamical systems.
Harmonic analysis.
Topology.
Analysis.
Mathematical Logic and Foundations.
Real Functions.
Dynamical Systems and Ergodic Theory.
Abstract Harmonic Analysis.
Topology.
QA299.6-433
515