A theorem of Piccard's type in abelian Polish groups (Q2400104)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A theorem of Piccard's type in abelian Polish groups |
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A theorem of Piccard's type in abelian Polish groups (English)
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25 August 2017
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The main result of this paper is: Let \((X, +, d)\) be an abelian Polish group. Let \(A\subset X\) be a Borel set which is not Haar meager. Then \(F_N(A):=\bigg\{(x_1,\dots,x_N) \in X^N:A\cap \bigcap\limits_{i=1}^{N} (A+x_1)\) is not Haar meager in \( X\bigg\}\) is a neighbourhood of \(0\) in \(X^N\) for every \(N\in\mathbb{N}\).
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Haar meager set
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Haar null set
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Piccard's theorem
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