Strassen disintegration theorems
The scalar valued disintegration theorem states that for a real vector space \(X\) and a measure space, if a linear functional \(\varphi\) on \(X\) has the property that \(\varphi(x)\) is dominated by \(\int{\mathfrak D}(x)d\mu\) for all \(x\) in \(X\) where \({\mathfrak D}\) is a sublinear operator from \(X\) into \(L^1(\mu)\), then there exists a linear operator \(T\) dominated by \({\mathfrak D}\) from \(X\) into \(L^1(\mu)\) so that \(\varphi(x)=\int T(x)d\mu\). \textit{M. Neumann} [Arch. Math. 29, 413-420 (1977; Zbl 0368.28013)] provided a generalization of this result. Here a more general version, not dependent on the Radon-Nikodym property, is provided in the setting of Riesz spaces. Several consequences of this generalization are considered.
not dependent on the Radon-Nikodym property
scientific article; zbMATH DE number 815695