Invariant Cocycles Have Abelian Ranges |
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Authors: | Gernot Greschonig and Klaus Schmidt |
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Affiliation: | (1) Math.Dept., UCLA, University of California, Los Angeles, CA 90095-155505, USA |
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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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