On additivity of mappings on measurable functions
Let \(\mathcal{K}\) be a hereditary cone in \(\mathfrak{M}^+\), where \(\mathfrak{M}=\mathfrak{M}(\Omega)\) is a vector space of measurable functions on \(\Omega\). The main result of the paper is the following. Let \(T:\mathcal{K}\rightarrow [0,\infty]\). Then, \(T\) is additive if and only if \(T\) is \(l\)-additive and regular. Moreover, the paper under review describes the relation between \(l\)-additive and monotone maps and the last section contains partial characterization of subadditive mappings.
scientific article; zbMATH DE number 6365596