# The Nikodym property and filters on ω

- Speaker(s)
**Tomasz Żuchowski**- Affiliation
- University of Wrocław
- Date
- June 12, 2024, 4:15 p.m.
- Room
- room 5050
- Seminar
- Topology and Set Theory Seminar

An infinite Boolean algebra A is said to have the Nikodym property when every pointwise bounded sequence of measures on A is uniformly bounded.

For a free filter F on ω we consider the space N_F = ω ∪ {p_F}, where ω is discrete and open neighborhoods of p_F are of the form X ∪ {p_F} for X ∈ F.

We define a property of the filter F which implies that any Boolean algebra A cannot have the Nikodym property when N_F is homeomorphically embedded into the Stone space St(A) of ultrafilters on A. We will characterize this property in terms of sequences of non-negative measures on ω, and in terms of exhaustive ideals associated to density submeasures on ω. Moreover, we will study the cofinal structure of the Katětov preorder on this class of filters.