A Polish group containing a Haar null $F_\sigma$-subgroup that cannot be enlarged to a Haar null $G_\delta$-set

@article{Banakh2016APG,
title={A Polish group containing a Haar null \$F\_\sigma\$-subgroup that cannot be enlarged to a Haar null \$G\_\delta\$-set},
author={Taras O. Banakh},
journal={arXiv: General Topology},
year={2016}
}

Answering a question of Elekes and Vidny\'anszky, we construct a Polish meta-abelian group $H$ and a subgroup $F\subset H$, which is a Haar null $F_\sigma$-set in $H$ that cannot be enlarged to a Haar null $G_\delta$-set.

We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of… Expand

Let G be an abelian Polish group, e.g., a separable Banach space. A subset X ⊂ G is called Haar null (in the sense of Christensen) if there exists a Borel set B ⊃ X and a Borel probability measure µ… Expand

It is shown that the concept of zero set for the Haar measure can be generalized to abelian Polish groups which are not necessarily locally compact. It turns out that these groups, in many respects,… Expand