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The existence of measures of a given cocycle, I: atomless, ergodic σ-finite 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 suitably non-trivial σ-finite measure μ on X such that, for every Borel injection ϕ whose graph is contained in E, ρ(ϕ−1(x),x)=[d(ϕ*μ)/dμ](x) μ-almost everywhere.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 5 , October 2008 , pp. 1599 - 1613
Copyright
Copyright © 2008 Cambridge University Press

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