Kechris / Miller Topics in Orbit Equivalence

Erscheinungsjahr 2004
ISBN: 978-3-540-44508-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1852, 138 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kechris, Alexander

Miller, Benjamin D.

Inhaltsverzeichnis

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