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. In addition, applications to the study of function spaces will be discussed.
Absolute continuity of non-additive measures and applications to function spaces
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. In addition, applications to the study of function spaces will be discussed.File in questo prodotto:
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