A Lebesgue decomposition for elements in a topological group

Thomas P. Dence

International Journal of Mathematics and Mathematical Sciences, 1980, vol. 3, 1-8

Abstract:

Our aim is to establish the Lebesgue decomposition for strongly-bounded elements in a topological group. In 1963 Richard Darst established a result giving the Lebesgue decomposition of strongly-bounded elements in a normed Abelian group with respect to an algebra of projection operators. Consequently, one can establish the decomposition of strongly-bounded additive functions defined on an algebra of sets. Analagous results follow for lattices of sets. Generalizing some of the techniques yield decompositions for elements in a topological group.

Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:608532

DOI: 10.1155/S0161171280000609

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