On mu- statistical uniform convergence and Dini's theorem

GÜLFIRAT M.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.52, no.21, pp.7744-7751, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 21
  • Publication Date: 2023
  • Doi Number: 10.1080/03610926.2022.2059684
  • Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.7744-7751
  • Keywords: Uniform convergence, Dini's theorem, statistical convergence, finitely additive measure
  • Ankara University Affiliated: Yes

Abstract

The present paper aims to study the uniform convergence of a sequence of functions via the mu- statistical uniform convergence where mu 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.