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The Classification of Hyperfinite Borel Equivalence Relations

Kechris, A. S. (1990) The Classification of Hyperfinite Borel Equivalence Relations. In: Séminaire d'initiation à l'analyse. Publications mathématiques de l'Université Pierre et Marie Curie. No.104. Université Pierre et Marie Curie , Paris, pp. 1-2.

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Let X be a standard Borel space and E a Borel equivalence relation on X. We call E hyperfinite if there is a Borel automorphism T of X such that xEy ⇔ ∃ n Є ℤ(T^nx = y). For Borel equivalence relations E,F on X, Y resp. we write E ⊑ F ⇔ 3 ƒ : X → Y(ƒ Borel, injective with E = ƒ^(-1)[F]) E ≈ F ⇔ E ⊑ F and F ⊑ E E ≅ F ⇔ ∃ ƒ :X → Y(ƒ a Borel isomorphism with E= ƒ^(-1)[F]) A Borel equivalence relation E on X is called smooth if there is a Borel map ƒ: X → Y (Y some standard Borel space) with xEy ⇔ ƒ(x) = ƒ(y).

Item Type:Book Section
Additional Information:© 1991 Université Pierre et Marie Curie. The above results will appear in a forthcoming paper by the author entitled The structure of hyperfinite Borel equivalence relations.
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Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR1217322
Series Name:Publications mathématiques de l'Université Pierre et Marie Curie
Issue or Number:104
Record Number:CaltechAUTHORS:20130626-124718433
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39107
Deposited By: Ruth Sustaita
Deposited On:26 Jun 2013 22:20
Last Modified:03 Oct 2019 05:04

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