Strong integral summability and the Stone-Čech compactification of the half-line

Abstract

An /-measure is a finitely additive nonnegative set function defined on a collection of subsets of [0, oo) which vanishes on bounded Lebesgue measurable sets. We define statistical convergence and convergence in density relative to an /-measure and use nonnegative regular integral summability methods to generate /-measures. We observe that, for a large class of regular integral summability methods, the notions of strong integral summability, convergence in density and statistical convergence (relative to the /-measure generated by the method) coincide for bounded functions.