# Convergence and submeasures in Boolean algebras

## TL;DR

This paper establishes a characterization of Boolean algebras that admit a strictly positive exhaustive submeasure through the property of their sequential topology being uniformly Frechet, linking algebraic and topological features.

## Contribution

It provides a new equivalence between the existence of a submeasure and a topological property in Boolean algebras.

## Key findings

- Boolean algebra has a strictly positive exhaustive submeasure iff it has a uniformly Frechet sequential topology.
- Connects algebraic submeasure properties with topological convergence.
- Advances understanding of the interplay between algebraic and topological structures in Boolean algebras.

## Abstract

A Boolean algebra carries a strictly positive exhaustive submeasure if and only if it has a sequential topology that is uniformly Frechet.