Equivalence of Brooks-Jewett, Vitali-Hahn-Saks and Nikodým convergence theorems for uniform semigroup-valued additive functions on a Boolean ring
For sequences of strongly bounded additive functions from a Boolean ring \({\mathcal R}\) having the subsequential interpolation property into a Hausdorff uniform commutative semigroup S, the authors prove the Brooks- Jewett theorem and show that the Brooks-Jewett theorem is equivalent with the Vitali-Hahn-Saks theorem and the Nikodým convergence theorem. In the case where \({\mathcal R}\) is a \(\sigma\)-ring of sets and S is a Hausdorff topological commutative group, the reslt is due to \textit{L. Drewnowski} [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 20, 725-731 (1972; Zbl 0243.28011)].
scientific article; zbMATH DE number 3989691