Convergence of sequences of functions having some generalized Pawlak properties.

Abstract

A function $f:\mathbb R \to \mathbb R$ has the property ${\mathcal M}_1$ (${\mathcal M}_2$) if the restricted function $f | D(f)$ ($f | D_{ap}(f)$) is monotone. ($D(f)$ $D_{ap}(f)$ denotes the set of all discontinuity points [the set of all approximate discontinuity points] of $f$.) In this article I investigate the uniform, pointwise and transfinite limits of sequences of functions with the property ${\cal M}_i$, $i = 1,2$.