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.
On the absolute continuity of additive and non-additive functions
CAVALIERE, Paola;
2014
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.File in questo prodotto:
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