3 papers
math.LO2026
On maximal families of independent sets with respect to asymptotic density
Jonathan M. Keith, Paolo Leonetti
We study families of subsets of which are independent with respect to the asymptotic density . We show, for instance, that there exists a maximal -inde…
math.FA2026
Completeness and additive property for submeasures
Jonathan M. Keith, Paolo Leonetti
Given an extended real-valued submeasure defined on a field of subsets of a given set, we provide necessary and sufficient conditions for which the pseudometric de…
math.GN2024
The pseudometric topology induced by upper asymptotic density
Jonathan M. Keith
Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which is complete. The collection of sets with asymptot…