On statistical exhaustiveness

We study statistical versions of several types of convergence of sequences of functions between two metric spaces. Special attention is devoted to statistical versions of recently introduced notions of exhaustiveness (Gregoriades and Papanastassiou (2008) [4]) and strong uniform convergence on a bornology (Beer and Levi (2009) [3]). We obtain a few results about the continuity of the statistical pointwise limit of a sequence of functions.