A Yosida-Hewitt like theorem for \(\perp\)-decomposable measures
\(\perp\)-decomposable measures, that is set-functions decomposable w.r. to a semigroup operation \(\perp\) on a real interval, were introduced by \textit{D. Dubois} and \textit{H. Prade} [Int. J. Gen. Syst. 8, 43-61 (1982; Zbl 0473.94023)] and \textit{S. Weber} [J. Math. Anal. Appl. 101, 114-138 (1984; Zbl 0614.28019)]. In this paper the authors dealt with the problem of restating the Yosida-Hewitt theorem in this larger framework, by splitting these measures in the maximal \(\sigma\)-\(\perp\)-decomposable part and in the pure \(\perp\)-decomposable part. To this purpose a direct construction is given that an actual generalization of Yosida-Hewitt theorem exhibits. Other propositions contained in the paper concern the lattice structure of classes of decomposable measures.
scientific article; zbMATH DE number 4152768