Statistical order limit points in Riesz spaces

Abstract

The concept of statistical order convergence of sequences in Riesz
spaces is introduced and studied. In the present paper, we define the
statistical order limit points of a sequence (x_n) as a vector x that is
the order limit of a subsequence (x_k)_{k\in K} of (x_n) such that the set
K does not have density zero. Moreover, we introduce the statistical
order cluster points of sequences in Riesz spaces, and also, we give
some relations between them.