On maldistributed sequences and meager ideals

We show that an ideal I on ω is meager if and only if the set of sequences ( x n ) taking values in a Polish space X for which all elements of X are I -cluster points of ( x n ) 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 in [J. Math. Anal. Appl. 541 (2025), 128667]. Lastly, we show that the analogue of the first part holds replacing ν with ‖ ⋅ ‖ φ , where φ is a lower semicontinuous submeasure.