Topics in Orbit Equivalence

• Κύριοι συγγραφείς: Kechris, Alexander (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Miller, Benjamin D. (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.
• Έκδοση: 1st ed. 2004.
• Σειρά: Lecture Notes in Mathematics, 1852
• Θέματα: Mathematical analysis.; Analysis (Mathematics).; Mathematical logic.; Functions of real variables.; Dynamics.; Ergodic theory.; Harmonic analysis.; Topology.; Analysis.; Mathematical Logic and Foundations.; Real Functions.; Dynamical Systems and Ergodic Theory.; Abstract Harmonic Analysis.

 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.