Thomas P. Dence, "A Lebesgue decomposition for elements in a topological group", International Journal of Mathematics and Mathematical Sciences, vol. 3, Article ID 608532, 8 pages, 1980. https://doi.org/10.1155/S0161171280000609
A Lebesgue decomposition for elements in a topological group
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.
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