We are concerned with a wide class of non-additive functions, namely quasi - triangular functions, defined on a Boolean ring and taking values into a topological space, where no algebraic structure is required. The aim of the paper is twofold. First we prove that in some sense this class is equivalent to that one of finitely additive functions valued into a topological Abelian group. Secondly we show that a Vitali-Hahn-Saks theorem holds for exhaustive elements of it.
Some new results in non-additive measure theory
CAVALIERE, Paola;
2009-01-01
Abstract
We are concerned with a wide class of non-additive functions, namely quasi - triangular functions, defined on a Boolean ring and taking values into a topological space, where no algebraic structure is required. The aim of the paper is twofold. First we prove that in some sense this class is equivalent to that one of finitely additive functions valued into a topological Abelian group. Secondly we show that a Vitali-Hahn-Saks theorem holds for exhaustive elements of it.File in questo prodotto:
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