On the absolute continuity of additive and non-additive functions

Abstract

We are concerned with the notions of absolute continuity in terms of $0$-continuity, and of $(\epsilon,\delta)$-continuity, with respect to a finitely additive function taking values into a topological commutative group. A sufficient condition for their equivalence is established. The non-additive case of functions with values into Hausdorff topological spaces is also investigated.