Low complexity Haar null sets without G_δ hulls in Z^ω

Donát Nagy

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arXiv · 1610.06741

Low complexity Haar null sets without G_δ hulls in Z^ω

Donát Nagy

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Abstract

We show that for every $2\le ξ<ω_1$ there exists a Haar null set in $\mathbb{Z}^ω$ that is the difference of two $\mathbfΠ^0_ξ$ sets but not contained in any $\mathbfΠ^0_ξ$ Haar null set. In particular, there exists a Haar null set in $\mathbb{Z}^ω$ that is the difference of two $G_δ$ sets but not contained in any $G_δ$ Haar null set. This partially answers a question of M. Elekes and Z. Vidnyánszky. To prove this, we also prove a theorem which characterizes the Haar null subsets of $\mathbb{Z}^ω$.

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BibTeX RIS

Donát Nagy. 2018-03-25. Low complexity Haar null sets without G_δ hulls in Z^ω. https://arxiv.org/abs/1610.06741

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