no. 3
Decomposition of group-valued additive set functions
Annales de l'Institut Fourier, Tome 22 (1972) no. 3, pp. 131-140.

Soit m une fonction additive définie sur un clan H à valeurs dans un groupe topologique commutatif séparé et soit K un idéal de H. On donne des conditions suffisantes pour que m soit la somme de deux fonctions additives, l’une essentiellement portée sur K, l’autre nulle sur K. Ce résultat est utilisé pour obtenir deux décompositions de Lebesgue. On indique aussi d’autres applications ainsi que la théorie correspondante pour les mesures extérieures.

Let m be an additive function on a ring H of sets, with values in a commutative Hausdorff topological group, and let K be an ideal of H. Conditions are given under which m can be represented as the sum of two additive functions, one essentially supported on K, the other vanishing on K. The result is used to obtain two Lebesgue-type decomposition theorems. Other applications and the corresponding theory for outer measures are also indicated.

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     title = {Decomposition of group-valued additive set functions},
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Traynor, Tim. Decomposition of group-valued additive set functions. Annales de l'Institut Fourier, Tome 22 (1972) no. 3, pp. 131-140. doi : 10.5802/aif.427. https://aif.centre-mersenne.org/articles/10.5802/aif.427/

[1] C.E. Rickart, Decomposition of additive set functions, Duke Math. Jour., 10 (1943), 653-665. | MR | Zbl

[2] M. Sion, Outer measures with values in a topological group, Proc. Lond. Math. Soc. (3), 19 (1969), 89-106. | MR | Zbl

[3] M. Sion, Group-valued outer measures, International Congress of Mathematicians, Nice, 1970. | Zbl

[4] T. Traynor, Absolute continuity for group-valued measures (to appear), Can. Math. Bull., 1973. | MR | Zbl

[5] T. Traynor, A general Hewitt-Yosida Decomposition, (to appear). Can. Jour. Math. | Zbl

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