Statistical limit superior and limit inferior

Abstract

Following the concept of statistical convergence and statistical cluster points of a sequence x, we give a definition of statistical limit superior and inferior which yields natural relationships among these ideas: e.g., x is statistically convergent if and only if st-liminfx = st-limsupx. The statistical core of x is also introduced, for which an analogue of Knopp's Core Theorem is proved. Also, it is proved that a bounded sequence that is C1-summable to its statistical limit superior is statistically convergent.