Statistical order convergence in Riesz spaces

Abstract

In this paper, we introduce the concepts of statistical monotone convergence and statistical order convergence in a Riesz space, and establish some basic facts. We show that the statistical order convergence and the statistical convergence in norm need not be equivalent in a normed Riesz space. Finally, we introduce the statistical order boundedness of a sequence in a Riesz space. © 2012 Versita Warsaw and Springer-Verlag Wien.