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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.
| Autorius: | Benjamin D. Miller, Alexander Kechris, |
| Serija: | Lecture Notes in Mathematics |
| Leidėjas: | Springer Berlin Heidelberg |
| Išleidimo metai: | 2004 |
| Knygos puslapių skaičius: | 148 |
| ISBN-10: | 3540226036 |
| ISBN-13: | 9783540226031 |
| Formatas: | 235 x 155 x 9 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Topics in Orbit Equivalence“
