2025/05/26 by Paolo Leonetti, Leonetti, Paolo · 1 voice
Mathematics · Computer Science · #Rings, Modules, and Algebras #Advanced Algebra and Logic #Approximation Theory and Sequence Spaces
paper · doi:10.1016/j.jmaa.2025.129748
openalex publication_date 2025/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/01/20
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.