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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

Thomas P. Dence
Thomas P. Dence*
Affiliation:
Bowling Green State University, Huron, Ohio
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Abstract

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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 295 - 298
Copyright
Copyright © Canadian Mathematical Society 1977

References

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