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The existence of measures of a given cocycle, II: probability measures

Published online by Cambridge University Press:  01 October 2008

BENJAMIN MILLER
BENJAMIN MILLER*
Affiliation:
UCLA Department of Mathematics, 520 Portola Plaza, Los Angeles, CA 90095-1555, USA (email: [email protected])
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Abstract

Given a Polish space X, a countable Borel equivalence relation E on X, and a Borel cocycle , we characterize the circumstances under which there is a probability measure μ on X such that ρ(ϕ−1(x),x)=[d(ϕ*μ)/dμ](x) μ-almost everywhere, for every Borel injection ϕ whose graph is contained in E.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 5 , October 2008 , pp. 1615 - 1633
Copyright
Copyright © 2008 Cambridge University Press

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