TY  - BOOK
AU  - Kechris,Alexander S.
ED  - SpringerLink (Online service)
TI  - Topics in Orbit Equivalence
T2  - Lecture Notes in Mathematics,
SN  - 9783540445081
AV  - QA8.9-10.3 
U1  - 511.3 23
PY  - 2004///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Harmonic analysis
KW  - Differentiable dynamical systems
KW  - Logic, Symbolic and mathematical
KW  - Topology
KW  - Mathematical Logic and Foundations
KW  - Real Functions
KW  - Dynamical Systems and Ergodic Theory
KW  - Abstract Harmonic Analysis
N1  - Preface -- I. Orbit Equivalence -- II. Amenability and Hyperfiniteness -- III. Costs of Equivalence Relations and Groups -- References -- Index
N2  - 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
UR  - http://dx.doi.org/10.1007/b99421
ER  -