- 期刊
A LEBESGUE DECOMPOSITION FOR ELEMENTS IN A TOPOLOGICAL GROUP
並列摘要
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 decomposiitons for elements in a topological group.
延伸閱讀
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