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Qualitative properties of ideal convergent subsequences and rearrangements. (English) Zbl 1399.40010
Summary: We investigate the Baire category of \(\mathcal{I}\)-convergent subsequences and rearrangements of a divergent sequence \(s = (s_n)\) of reals if \(\mathcal{I}\) is an ideal on \(\mathbb{N}\) having the Baire property. We also discuss the measure of the set of \(\mathcal{I}\)-convergent subsequences for some classes of ideals on \(\mathbb{N}\). Our results generalize theorems due to H. I. Miller and C. Orhan [Acta Math. Hung. 93, No. 1–2, 135–151 (2001; Zbl 0989.40002)].

MSC:
40A35 Ideal and statistical convergence
40A05 Convergence and divergence of series and sequences
54E52 Baire category, Baire spaces
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
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