Topics in Orbit Equivalence. 1st ed. 2004

種類:

電子ブック

責任表示:

by Alexander Kechris, Benjamin D. Miller

出版情報:

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

著者名:

• Kechris, Alexander.
• Miller, Benjamin D.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1852

ISBN:

9783540445081 [3540445080]    

注記:

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