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A Lebesgue Decomposition for Vector Valued Additive Set Functions Defined on a Lattice
Published online by Cambridge University Press: 20 November 2018
Abstract
Our aim is to establish the Lebesgue decomposition for s-bounded vector valued additive functions defined on lattices of sets in both the finitely and countably additive setting. Strongly bounded (s-bounded) set functions were first studied by Rickart [15], and then by Rao [14], Brooks [1] and Darst [5; 6]. In 1963 Darst [6] established a result giving the decomposition of s-bounded elements in a normed Abelian group with respect to an algebra of projection operators.
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- Copyright © Canadian Mathematical Society 1977
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