ENGLISH

Topics in orbit equivalence

By Alexander S. Kechris (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
2004
ISBN
9783540226031, 3540226036
DOI
10.1007/b99421
LCC
QA3 .L28 no. 1852
Open Library ID
OL3315440M
Language
english
Format
PDF
Filesize
793 kB (811665 bytes)
Series
Lecture Notes in Mathematics 1852
Edition
1
Pages
138\141
Library
Kolxo3
Time added
2010-07-29 05:14:56
Mathematical Logic and Foundations; Real Functions

Description

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.

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