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 $\mu -$ 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 $\mu -$ statistical uniform convergence of a sequence of functions is characterized by that of another decreasing sequence of functions.

Keywords:

• Uniform convergence
• Dini’s theorem
• statistical convergence
• finitely additive measure

MATHEMATICS SUBJECT CLASSIFICATION 2020::

• 40A35
• 40G15
• 40A30
• 60B10
• 28B99