We are concerned with the notions of absolute continuity (in terms of zero-continuity and of epsilon-delta-continuity) of a function with respect to a finitely additive one 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.
On the absolute continuity of additive and non-additive functions / DE SIMONE, Anna; DE LUCIA, Paolo; Cavaliere, Paola. - In: FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI. - ISSN 0208-6573. - 50:1(2014), pp. 181-190. [10.7169/facm/2014.50.1.7]
On the absolute continuity of additive and non-additive functions
De Simone Anna;de Lucia Paolo;
2014
Abstract
We are concerned with the notions of absolute continuity (in terms of zero-continuity and of epsilon-delta-continuity) of a function with respect to a finitely additive one 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.File in questo prodotto:
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