Abstract.
Let R be a discrete nonsingular equivalence relation on a standard probability space , and let V be an ergodic strongly asymptotically central automorphism of R. We prove that every V-invariant cocycle with values in a Polish group G takes values in an abelian subgroup of G.
The hypotheses of this result are satisfied, for example, if A is a finite set, a closed, shift-invariant subset, V is the shift, μ a shift-invariant and ergodic probability measure on X, the two-sided tail-equivalence relation on X, a shift-invariant subrelation which is μ-nonsingular, and a shift-invariant cocycle.
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(Received 15 September 2001)
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Greschonig, G., Schmidt, K. Invariant Cocycles Have Abelian Ranges. Mh Math 134, 207–216 (2002). https://doi.org/10.1007/s605-002-8257-z
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DOI: https://doi.org/10.1007/s605-002-8257-z