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On some classical theorems in measure theory. (English) Zbl 0771.28005

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.

MSC:

28A33 Spaces of measures, convergence of measures
28B05 Vector-valued set functions, measures and integrals
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