Alexander Kechris, Benjamin D. Miller

Topics in Orbit Equivalence (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 138
• Erscheinungstermin: 8. September 2004
• Englisch
• ISBN-13: 9783540445081
• Artikelnr.: 53386898

Autorenporträt

Alexander S. Kechris, California Institute of Technology, Pasadena, PA, USA / Benjamin D. Miller, University of California, Los Angeles, CA, USA

Inhaltsangabe

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