Inner and outer representation by Choquet integral
A non-additive measure \(\mu\) is \(i\)-regular, if its values at a compact set \(C\) can be aproximated by values \(\mu (O)\), where \(O\) is an open set, \(C \subseteq O\). In a similar way an \(o\)-regular non-additive measure is defined, where its values at an open set \(O\) can be aproximated by values \(\mu (C)\), where \(C\) is as above. Representation theorems of a comonotone additive and monotone function by a Choquet integral are shown using \(o\)-regular and \(i\)-regular non-additive measures. Also the representation of a comonotone additive monotone functional is shown.
scientific article; zbMATH DE number 5149450