Statistical Limit Superior and Limit Inferior

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