Popa, Dumitru On some classical theorems in measure theory. (English) Zbl 0771.28005 Bull. Pol. Acad. Sci., Math. 40, No. 4, 255-263 (1992). Summary: In this paper we present some results equivalent with the well-known Vitali-Hahn-Saks theorem in both cases of \(\sigma\)-Boolean algebras and Boolean algebras. In addition, we prove extensions from \(\sigma\)-Boolean algebras to Boolean algebras with the so-called VHS property of some classical results in measure theory.Using the Vitali-Hahn-Saks theorem we also prove that the space of unconditionally convergent series of a Banach space with the Schur property has itself the Schur property. Cited in 1 Document MSC: 28A33 Spaces of measures, convergence of measures 28B05 Vector-valued set functions, measures and integrals Keywords:Grothendiek space; vector measure; additive set function; \(\sigma\)- Boolean algebras; Vitali-Hahn-Saks theorem; Boolean algebras; extensions; Banach space; Schur property PDFBibTeX XMLCite \textit{D. Popa}, Bull. Pol. Acad. Sci., Math. 40, No. 4, 255--263 (1992; Zbl 0771.28005)