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A theorem of Piccard’s type in abelian Polish groups

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Abstract

In the paper we prove a theorem of Piccard’s type which generalizes [9, Theorem 2]. More precisely, we show that in an abelian Polish group X the set \(\left\{ {\left( {{x_{1, \ldots ,\;}}{x_N}} \right) \in \;{X^N}\;:\;A\; \cap \;\bigcap\limits_{i = 1}^N {\left( {A + {x_i}} \right)} \;is\;not\;Haar\;meager\;in\;X} \right\}\) is a neighbourhood of 0 for every N ∈ N and every Borel non-Haar meager set A ⊂ X. The paper refers to the paper [3].

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  1. Department of Mathematics, Rzeszów University of Technology, Powstańców Warszawy 12, 35-959, Rzeszów, Poland

    E. Jabłońska

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  1. E. Jabłońska
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Correspondence to E. Jabłońska.

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Jabłońska, E. A theorem of Piccard’s type in abelian Polish groups. Anal Math 42, 159–164 (2016). https://doi.org/10.1007/s10476-016-0204-z

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  • DOI: https://doi.org/10.1007/s10476-016-0204-z

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