International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1980 / Article

Open Access

Volume 3 |Article ID 608532 | https://doi.org/10.1155/S0161171280000609

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

Received03 May 1979
Revised29 Feb 1980

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.

Copyright © 1980 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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