1.

Record Nr.

UNINA9910144617803321

Autore

Kechris Alexander

Titolo

Topics in Orbit Equivalence [[electronic resource] /] / by Alexander Kechris, Benjamin D. Miller

Pubbl/distr/stampa

Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2004

ISBN

3-540-44508-0

Edizione

[1st ed. 2004.]

Descrizione fisica

1 online resource (X, 138 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1852

Disciplina

515.48

Soggetti

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

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references (pages 129-130) and index.

Nota di contenuto

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

Sommario/riassunto

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.