# 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

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topGreschonig, 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 -

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