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On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type

Published online by Cambridge University Press:  20 November 2018

Radu-Bogdan Munteanu
Radu-Bogdan Munteanu*
Affiliation:
University of Bucharest, Faculty of Chemistry, Department of Physics and Applied Mathematics, 4-12 Bd. Regina Elisabeta, 030018, Sector 1, Bucharest, Romania e-mail: radu-bogdan.munteanu@g.unibuc.ro
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Abstract

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Product type equivalence relations are hyperfinite measured equivalence relations, which, up to orbit equivalence, are generated by product type odometer actions. We give a concrete example of a hyperfinite equivalence relation of non-product type, which is the tail equivalence on a Bratteli diagram. In order to show that the equivalence relation constructed is not of product type we will use a criterion called property $\text{A}$. This property, introduced by Krieger for non-singular transformations, is defined directly for hyperfinite equivalence relations in this paper.

Keywords

37A2037A3546L10property Ahyperfinite equivalence relationnon-product type
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 1 , 01 March 2013 , pp. 136 - 147
Copyright
Copyright © Canadian Mathematical Society 2013

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