Topics in Orbit Equivalence

Released on by Alexander S. Kechris
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  • Topics in Orbit Equivalence Book Detail

  • Author : Alexander S. Kechris
  • Release Date : 2004-08-26
  • Publisher : Springer Science & Business Media
  • Genre : Computers
  • Pages : 148
  • ISBN 13 : 9783540226031
  • File Size : 67,67 MB
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Topics in Orbit Equivalence by Alexander S. Kechris PDF Summary

Book 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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