论文信息 - Amenable versus hyperfinite Borel equivalence relations

Amenable versus hyperfinite Borel equivalence relations

Let X be a standard Borel space (i.e., a Polish space with the associated Borel structure), and let E be a countable Borel equivalence relation on X, i.e., a Borel equivalence relation E for which every equivalence class [X]_E is countable. By a result of Feldman-Moore [FM], E is induced by the orbits of a Borel action of a countable group G on X.

Alexander S. Kechris | A. Kechris

[1] J. Feldman,et al. Ergodic equivalence relations, cohomology, and von Neumann algebras , 1975 .

[2] V. Varadarajan,et al. Groups of automorphisms of Borel spaces , 1963 .

[3] Theodore A. Slaman,et al. Definable functions on degrees , 1988 .

[4] Alexander S. Kechris. Amenable Equivalence Relations and Turing Degrees , 1991, J. Symb. Log..

[5] R. Dougherty,et al. The structure of hy-per nite Borel equivalence relations , 1994 .

[6] Calvin C. Moore,et al. Ergodic equivalence relations, cohomology, and von Neumann algebras. II , 1977 .

[7] Alain Louveau,et al. A Glimm-Effros dichotomy for Borel equivalence relations , 1990 .

[8] Benjamin Weiss,et al. An amenable equivalence relation is generated by a single transformation , 1981, Ergodic Theory and Dynamical Systems.

[9] R. Zimmer. Hyperfinite factors and amenable ergodic actions , 1977 .

[10] M. Nadkarni. On the existence of a finite invariant measure , 1990 .

[11] R. Lyons,et al. Amenability, Kazhdan’s property and percolation for trees, groups and equivalence relations , 1991 .

[12] Benjamin Weiss,et al. Ergodic theory of amenable group actions. I: The Rohlin lemma , 1980 .

[13] A. Kechris. The Structure of Borel Equivalence Relations in Polish Spaces , 1992 .