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 . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-11,
author = {S\l awomir Solecki},
title = {Haar null and non-dominating sets},
journal = {Fundamenta Mathematicae},
volume = {167},
year = {2001},
pages = {197-217},
zbl = {0994.28006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-11}
}
Sławomir Solecki. Haar null and non-dominating sets. Fundamenta Mathematicae, Tome 167 (2001) pp. 197-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm170-1-11/