On some representations of almost everywhere continuous functions on $\mathbb R^m$

Ewa Strońska¹

¹ Institute of Mathematics Kazimierz Wielki University Plac Weyssenhoffa 11 85-072 Bydgoszcz, Poland

Colloquium Mathematicum, Tome 105 (2006) no. 2, pp. 319-331.

Résumé

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

Détail

DOI : 10.4064/cm105-2-12

Keywords: proved following conditions equivalent almost everywhere continuous function mathbb where strongly quasicontinuous mathbb where mathbb strongly quasicontinuous nbsp mathbb