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}
}
  • T. Banakh
  • Published 1 April 2016
  • Mathematics
  • arXiv: General Topology
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. 
1 Citations
Haar null and Haar meager sets: a survey and new results
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

References

SHOWING 1-3 OF 3 REFERENCES
Haar null sets without Gδ hulls
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
On sets of Haar measure zero in abelian polish groups
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,
E-mail address: t.o.banakh@gmail