Ideals in the set of natural numbers and the Baire category in selected function spaces
Investigation of a new class of ideals on N of density-type with weight, called simple density ideals. Investigation of ideal invariant injections from N to N and their properties. Investigation of the Baire category of integrable functions with the Lesigne property. Investigation of the Baire category and Lebesgue measure of ideal convergent subsequences (subseries) and rearrangements of divergent sequences (series) under the respective assumptions on an ideal. Investigations of relationships between ideal cluster points and ideal limit points.
Defended PhD thesis, Michał Popławski, 2018.
Marek Balcerzak, Pratulananda Das, Małgorzata Filipczak, Jarosław Swaczyna, Generalized kinds of density and the associated ideals, Acta Math. Hungar., 147 (2015), 97-115.
Marek Balcerzak, Szymon Głąb, Artur Wachowicz, Qualitative properties of ideal convergent subsequences and rearrangements, Acta Math. Hungar. 150 (2016), 312-323.
Marek Balcerzak, Adam Majchrzycki, Filip Strobin, Typical behaviour of integrable functions at infinity, Indag. Math. 27 (2016), 893-901.
Marek Balcerzak, Szymon Głąb, Jarosław Swaczyna, Ideal invariant injections, J. Math. Anal. Appl. 445 (2017), 423-442.
Marek Balcerzak, Michał Popławski, Artur Wachowicz, The Baire category of ideal convergent subseries and rearrangements. Topology Appl. 231(2017), 219-230.
Marek Balcerzak, Michał Popławski, Artur Wachowicz, Ideal convergent subsequences and rearrangements for divergent sequences of functions, Math. Slovaca 67(2017), 1461-1468.
Marek Balcerzak, Małgorzata Filipczak, Ideal convergence of sequences and some of its applications, Folia Math. 19(2017), 3-8.
Marek Balcerzak, Paolo Leonetti, On the relationship between ideal cluster points and ideal limit points. Topology Appl. 252(2019), 178-190.
Adam Kwela, Michał Popławski, Jarosław Swaczyna, Properties of simple density ideals. J. Math. Anal. Appl. 477(2019), 551-575.
Marek Balcerzak, Paolo Leonetti, The Baire category of subsequences and permutations which preserve limit points, Results Math (2020) 75:171.
Marek Balcerzak, Paolo Leonetti, A Tauberian theorem for ideal statistical convergence, Indag. Math. 31 (2020), 83-95.