A Converse to Dye's Theorem
Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of F<sub>2</sub> on a standard Borel probability space is orbit equivalent to an action of a countable grou...
| Veröffentlicht in: | Transactions of the American Mathematical Society. - American Mathematical Society, 1900. - 357(2005), 8, Seite 3083-3103 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2005
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| Zugriff auf das übergeordnete Werk: | Transactions of the American Mathematical Society |
| Schlagworte: | Ergodic Theory Treeable Equivalence Relations Non-Amenable Groups Property T Groups Free Groups Borel Reducibility Philosophy Applied sciences Mathematics Behavioral sciences |
| Zusammenfassung: | Every non-amenable countable group induces orbit inequivalent ergodic equivalence relations on standard Borel probability spaces. Not every free, ergodic, measure preserving action of F<sub>2</sub> on a standard Borel probability space is orbit equivalent to an action of a countable group on an inverse limit of finite spaces. There is a treeable non-hyperfinite Borel equivalence relation which is not universal for treeable in the <tex-math>$\leq_B$</tex-math> ordering. |
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| ISSN: | 10886850 |