Ergodic decomposition of quasi-invariant probability measures

Gernot Greschonig; Klaus Schmidt

Colloquium Mathematicae (2000)

  • Volume: 84/85, Issue: 2, page 495-514
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Greschonig, Gernot, and Schmidt, Klaus. "Ergodic decomposition of quasi-invariant probability measures." Colloquium Mathematicae 84/85.2 (2000): 495-514. <http://eudml.org/doc/210829>.

@article{Greschonig2000,
abstract = {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.},
author = {Greschonig, Gernot, Schmidt, Klaus},
journal = {Colloquium Mathematicae},
keywords = {ergodic decomposition; nonsingular group actions; nonsingular equivalence relations; quasi-invariant measures; quasi-invariant measure},
language = {eng},
number = {2},
pages = {495-514},
title = {Ergodic decomposition of quasi-invariant probability measures},
url = {http://eudml.org/doc/210829},
volume = {84/85},
year = {2000},
}

TY - JOUR
AU - Greschonig, Gernot
AU - Schmidt, Klaus
TI - Ergodic decomposition of quasi-invariant probability measures
JO - Colloquium Mathematicae
PY - 2000
VL - 84/85
IS - 2
SP - 495
EP - 514
AB - 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.
LA - eng
KW - ergodic decomposition; nonsingular group actions; nonsingular equivalence relations; quasi-invariant measures; quasi-invariant measure
UR - http://eudml.org/doc/210829
ER -

References

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