On Constructing Ergodic Hyperfinite Equivalence Relations of Non-Product Type
Printed: Mar 2013
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 A. This
property, introduced by Krieger for non-singular transformations, is
defined directly for hyperfinite equivalence relations in this paper.
property A, hyperfinite equivalence relation, non-product type
37A20 - Orbit equivalence, cocycles, ergodic equivalence relations
37A35 - Entropy and other invariants, isomorphism, classification
46L10 - General theory of von Neumann algebras