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Topics in orbit equivalence

Author: A S Kechris
Publisher: Berlin ; New York : Springer, ©2004.
Series: Lecture notes in mathematics (Springer-Verlag), 1852.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This volume provides a self-contained introduction to some topics in orbit equivalence theory, a branch of ergodic theory. The final chapter is a detailed account of Gaboriau's recent results on the  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: A S Kechris
ISBN: 3540226036 9783540226031
OCLC Number: 56492332
Description: x, 134 pages ; 24 cm.
Contents: I. Orbit equivalence --
1. Group actions and equivalence relations --
2. Invariant measures --
3. Ergodicity --
4. Isomorphism and orbit equivalence --
II. Amenability and hyperfiniteness --
5. Amenable groups --
6. Hyperfiniteness --
7. Dye's theorem --
8. Quasi-invariant measures --
9. Amenable equivalence relations --
10. Amenability vs. hyperfiniteness --
11. Groups of polynomial growth --
12. Generic hyperfiniteness --
13. Generic compressibility --
III. Costs of equivalence relations and groups --
14. Preliminaries --
15. Countable Borel equivalence relations --
16. More on invariant measures --
17. Graphings of equivalence relations --
18. Cost of an equivalence relation --
19. Treeings of an equivalence relation --
20. The cost of a smooth equivalence relation --
21. The cost of a complete section --
22. Cost and hyperfiniteness --
23. Joins --
24. Commuting equivalence relations --
25. Subequivalence relations of finite index --
26. Cheap equivalence relations --
27. Free and amalgamated joins --
28. Costs and free actions --
29. Cost of a group --
30. Treeable groups --
31. Cost and amenable groups --
32. Generating subgroups --
33. Products --
34. Subgroups of finite index --
35. Cheap groups --
36. Free and amalgamated products --
37. HNN-extensions --
38. A list of open problems.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1852.
Responsibility: Alexander S. Kechris, Benjamin D. Miller.
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