Geodesic
Ergodic decomposition of quasi-invariant probability measures
Colloquium Mathematicum, Tome 84 (2000) no. 2, pp. 495-514
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The purpose of this note is to prove various versions of the ergodic decomposition theorem for probability measures on standard Borel spaces which are quasi-invariant under a Borel action of a locally compact second countable group or a discrete nonsingular equivalence relation. In the process we obtain a simultaneous ergodic decomposition of all quasi-invariant probability measures with a prescribed Radon-Nikodym derivative, analogous to classical results about decomposition of invariant probability measures.
DOI : 10.4064/cm-84/85-2-495-514
Keywords: ergodic decomposition, nonsingular group actions, nonsingular equivalence relations, quasi-invariant measures 
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Gernot Greschonig; Klaus Schmidt. Ergodic decomposition of quasi-invariant probability measures. Colloquium Mathematicum, Tome 84 (2000) no. 2, pp. 495-514. doi: 10.4064/cm-84/85-2-495-514

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