A generic threshold phenomena in weighted $\ell^2$

TL;DR

This paper explores threshold phenomena in weighted -spaces, presenting a Baire category version of a topological theorem that is shown to be optimal in multiple respects.

Contribution

It introduces a summable Baire category version of Kf6rner's topological Ivashev-Musatov Theorem, advancing the understanding of threshold phenomena in weighted -spaces.

Findings

Established a Baire category version of the theorem.

Proved the optimality of the main result.

Enhanced theoretical understanding of threshold phenomena.

Abstract

We consider threshold phenomenons in the context of weighted $\ell^2$-spaces. Our main result is a summable Baire category version of K\"orner's topological Ivashev-Musatov Theorem, which is proved to be optimal from several aspects.