On maldistributed sequences and meager ideals

We show that an ideal I on ω is meager if and only if the set of sequences (xn) taking values in a Polish space X for which all elements of X are I-cluster points of (xn) is comeager. The latter condition is also known as ν-maldistribution, where ν : P(ω) → R is the {0, 1}-valued submeasure defined by ν(A)=1 if and only if A /∈ I. It turns out that the meagerness of I is also equivalent to a technical condition given by Mišík and Tóth (2025) [19]. Lastly, we show that the analogue of the first part holds replacing ν with ·ϕ, where ϕ is a lower semicontinuous submeasure