Ergodic decomposition of quasi-invariant probability measures

Volume 84 / 2000

Gernot Greschonig, Klaus Schmidt Colloquium Mathematicum 84 (2000), 495-514 DOI: 10.4064/cm-84/85-2-495-514


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.


  • Gernot Greschonig
  • Klaus Schmidt

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