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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...
Contents. 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...
Contents. 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 ...
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