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.

#### 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.
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2014
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/3992655
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