Daniell integral represented by Radon measures
Let X be a Suslin space and L be a sublattice of C(X) such that for every \(x\in X\) there exists a function \(\phi\in L\) for which \(\phi\) (x)\(\neq 0\). It is shown that for any Daniell integral \(\mu\) : \(L\to {\mathbb{R}}\) there exists a Radon measure m on X such that \(L\subset {\mathcal L}^ 1(m)\) and \[ \mu (\phi)=\int \phi dm,\quad \forall \phi \in L. \] Moreover, the measure m may be uniquely determined by constraining it to be concentrated on a certain type of subset of X. The relation between \({\mathcal L}^ 1(m)\) and \({\mathcal L}^ 1(\mu)\) is examined in detail.
scientific article; zbMATH DE number 4109069