On Dieudonné's boundedness theorem
The author proves a version of Dieudonné's boundedness theorem for group-valued finitely additive regular set functions defined on a field \({\mathfrak U}\). Regularity is defined with respect to two sublattices \({\mathfrak F}\) and \({\mathfrak G}\) of \({\mathfrak U}\), which satisfy certain conditions and correspond in a topological setting to the systems of closed and open sets, respectively. In the special case of \({\mathfrak F}={\mathfrak G}={\mathfrak U}\) one gets Nikodým's boundedness theorem for set functions defined on an algebra satisfying the ``subsequential interpolation property''.
group-valued finitely additive regular set functions
scientific article; zbMATH DE number 4142369
scientific article