Jacek Marchwicki

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20162022

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math.CA2022

Set of uniqueness for Cantorvals

Szymon Glab, Jacek Marchwicki

The main result is that the celebrated Guthrie-Nymann's Cantorval has comeager set of uniqueness. On the other hand many other Cantorvals have meager set of uniqueness.

math.CA2019

Cardinal functions of purely atomic measures

Szymon Głab, Jacek Marchwicki

Let $μ$ be a purely atomic measure. By $f_{μ} : [0, \infty) \to {0, 1, 2, \dots, ω, c}$ we denote its cardinal function $f_{μ} (t) = ∣ {A \subset N : μ (A) = t} ∣$ . We study t…