Výsledky vyhledávání - "Wachowicz, Artur"

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Baire Category Lower Density Operators with Borel Values

Autor: Balcerzak, Marek, Hejduk, Jacek, Wachowicz, Artur

We prove that the lower density operator associated with the Baire category density points in the real line has Borel values of class $\pmb \Pi^0_3$ which is analogous to the measure case. We also introduce the notion of the Baire category density po

Externí odkaz: http://arxiv.org/abs/2207.06821

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Ideal convergent subseries in Banach spaces

Autor: Balcerzak, Marek, Popławski, Michał, Wachowicz, Artur

Assume that $\mathcal{I}$ is an ideal on $\mathbb{N}$, and $\sum_n x_n$ is a divergent series in a Banach space $X$. We study the Baire category, and the measure of the set $A(\mathcal{I}):=\left\{t \in \{0,1\}^{\mathbb{N}} \colon \sum_n t(n)x_n \tex

Externí odkaz: http://arxiv.org/abs/1803.03699

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Ideal convergent subsequences and rearrangements for divergent sequences of functions

Autor: Balcerzak, Marek, Popławski, Michał, Wachowicz, Artur

Let $\I$ be an ideal on $\N$ which is either analytic or coanalytic. Assume that $(f_n)$ is a sequence of functions with the Baire property from a Polish space $X$ into a complete metric space $Z$, which is divergent on a comeager set. We investigate

Externí odkaz: http://arxiv.org/abs/1604.08359

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