On μ– statistical uniform convergence and Dini’s theorem

Abstract

The present paper aims to study the uniform convergence of a sequence of functions via the statistical uniform convergence where μ is a finitely additive set function defined on a field of subsets of positive integers. In particular we deal with an analog of Dini’s theorem. It turns out that statistical uniform convergence of a sequence of functions is characterized by that of another decreasing sequence of functions.