English

Haar-positive closed subsets of Haar-positive analytic sets

Logic 2020-03-17 v1 Group Theory

Abstract

We show that every non-Haar-null analytic subset of Zω\mathbb{Z}^\omega contains a non-Haar-null closed subset. Moreover, we also prove that the codes of Haar-null analytic subsets, and, consequently, closed Haar-null sets in the Effros Borel space of Zω\mathbb{Z}^\omega form a Δ21\mathbf{\Delta}^1_2 set.

Cite

@article{arxiv.2003.06854,
  title  = {Haar-positive closed subsets of Haar-positive analytic sets},
  author = {Márton Elekes and Márk Poór and Zoltán Vidnyánszky},
  journal= {arXiv preprint arXiv:2003.06854},
  year   = {2020}
}
R2 v1 2026-06-23T14:15:17.662Z