Haar null and non-dominating sets

Sławomir Solecki. "Haar null and non-dominating sets." Fundamenta Mathematicae 170.1-2 (2001): 197-217. <http://eudml.org/doc/281992>.

@article{SławomirSolecki2001,
abstract = {We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of $ω^\{ω\}$. Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain results connecting Haar null sets on countable products of locally compact Polish groups with amenability of the factor groups.},
author = {Sławomir Solecki},
journal = {Fundamenta Mathematicae},
keywords = {non-dominating set; Haar null sets; Polish group},
language = {eng},
number = {1-2},
pages = {197-217},
title = {Haar null and non-dominating sets},
url = {http://eudml.org/doc/281992},
volume = {170},
year = {2001},
}

TY - JOUR
AU - Sławomir Solecki
TI - Haar null and non-dominating sets
JO - Fundamenta Mathematicae
PY - 2001
VL - 170
IS - 1-2
SP - 197
EP - 217
AB - We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of $ω^{ω}$. Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain results connecting Haar null sets on countable products of locally compact Polish groups with amenability of the factor groups.
LA - eng
KW - non-dominating set; Haar null sets; Polish group
UR - http://eudml.org/doc/281992
ER -