Extensions of generic measure-preserving actions

Julien Melleray[1]

  • [1] Université de Lyon CNRS UMR 5208 Institut Camille Jordan 43 boulevard du 11 novembre 1918 69622 Villeurbanne Cedex (France)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 2, page 607-623
  • ISSN: 0373-0956

Abstract

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We show that, whenever Γ is a countable abelian group and Δ is a finitely-generated subgroup of Γ , a generic measure-preserving action of Δ on a standard atomless probability space ( X , μ ) extends to a free measure-preserving action of Γ on ( X , μ ) . This extends a result of Ageev, corresponding to the case when Δ is infinite cyclic.

How to cite

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Melleray, Julien. "Extensions of generic measure-preserving actions." Annales de l’institut Fourier 64.2 (2014): 607-623. <http://eudml.org/doc/275510>.

@article{Melleray2014,
abstract = {We show that, whenever $\Gamma $ is a countable abelian group and $\Delta $ is a finitely-generated subgroup of $\Gamma $, a generic measure-preserving action of $\Delta $ on a standard atomless probability space $(X, \mu )$ extends to a free measure-preserving action of $\Gamma $ on $(X, \mu )$. This extends a result of Ageev, corresponding to the case when $\Delta $ is infinite cyclic.},
affiliation = {Université de Lyon CNRS UMR 5208 Institut Camille Jordan 43 boulevard du 11 novembre 1918 69622 Villeurbanne Cedex (France)},
author = {Melleray, Julien},
journal = {Annales de l’institut Fourier},
keywords = {Measure-preserving action; Baire category; Polish group; measure-preserving group action},
language = {eng},
number = {2},
pages = {607-623},
publisher = {Association des Annales de l’institut Fourier},
title = {Extensions of generic measure-preserving actions},
url = {http://eudml.org/doc/275510},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Melleray, Julien
TI - Extensions of generic measure-preserving actions
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 2
SP - 607
EP - 623
AB - We show that, whenever $\Gamma $ is a countable abelian group and $\Delta $ is a finitely-generated subgroup of $\Gamma $, a generic measure-preserving action of $\Delta $ on a standard atomless probability space $(X, \mu )$ extends to a free measure-preserving action of $\Gamma $ on $(X, \mu )$. This extends a result of Ageev, corresponding to the case when $\Delta $ is infinite cyclic.
LA - eng
KW - Measure-preserving action; Baire category; Polish group; measure-preserving group action
UR - http://eudml.org/doc/275510
ER -

References

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