Geodesic
A decomposition theorem for submeasures
Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 69-74

Voir la notice de l'article provenant de la source Cambridge University Press

In recent years versions of the Lebesgue and the Hewitt-Yosida decomposition theorems have been proved for group-valued measures. For example, Traynor [4], [6] has established Lebesgue decomposition theorems for exhaustive groupvalued measures on a ring using (1) algebraic and (2) topological notions of continuity and singularity, and generalizations of the Hewitt-Yosida theorem have been given by Drewnowski [2], Traynor [5] and Khurana [3]. In this paper we consider group-valued submeasures and in particular we have established a decomposition theorem from which analogues of the Lebesgue and Hewitt-Yosida decomposition theorems for submeasures may be derived. Our methods are based on those used by Drewnowski in [2] and the main theorem established generalizes Theorem 4.1 of [2]. 
Khan, A. R.; Rowlands, K. A decomposition theorem for submeasures. Glasgow mathematical journal, Tome 26 (1985) no. 1, pp. 69-74. doi: 10.1017/S0017089500005784
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[1] 1.Drewnowski, L., Topological rings of sets, continuous set functions, integration I, Bull. Acad. Polon. Sci., Ser. Sci. Math.,, Astr. et Phys., 20, (1972), 269–276. Google Scholar

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[6] 6.Traynor, T., The Lebesgue decomposition for group-valued set functions, Trans. Amer. Math. Soc. 220 (1976), 307–319. Google Scholar | DOI

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