Author | Kechris, Alexander S. author |
---|---|

Title | Topics in Orbit Equivalence [electronic resource] / by Alexander S. Kechris |

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

Connect to | http://dx.doi.org/10.1007/b99421 |

Descript | X, 138 p. online resource |

SUMMARY

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

CONTENT

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

Mathematics
Mathematical analysis
Analysis (Mathematics)
Harmonic analysis
Dynamics
Ergodic theory
Functions of real variables
Mathematical logic
Topology
Mathematics
Analysis
Mathematical Logic and Foundations
Real Functions
Dynamical Systems and Ergodic Theory
Abstract Harmonic Analysis
Topology