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#Toeplitz subshift orbit equivalence how to#
However, it is notĬlear how to conclude anything from that about theĮquivalence relation E in particular, we do not know Not embed the groupoid of the free part of any BernoulliĪction of an infinite property (T) group. Results, it is easy to prove that Γ does For example, using Popa’s cocycle superrigidity Α 0 gives some restrictions on the groupoid We finally observe that the existence of the cocycle Its arrows as the other information can be recovered from We will sometimes identify a groupoid with the set of Will denote by A ( x, y ) the set of arrows between x and Such that P n ( x ) enumerate s − 1 ( x ) and Q n ( x )Įnumerate r − 1 ( x ) for every x. Of Borel maps P n : X → A and Q n : X → A The Lusin–Novikov selection theorem, there exist sequences
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