On some representations of a.e. continuous functions

Abstract

It is proved that the following conditions are equivalent: (a) \(f\) is an almost everywhere continuous function; (b) \(f=g+h\), where \(g,h\) are strongly quasi-continuous; and, (c) \(f=c+gh\), where \(c \in \mathbb{R}\) and \(g,h\) are s.q.c..