Decomposition of group-valued additive set functions

Traynor, Tim

doi:10.5802/aif.427

Traynor, Tim

Annales de l'Institut Fourier, Volume 22 (1972) no. 3, pp. 131-140.

Abstract
Résumé

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.

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.

MR Zbl

DOI: 10.5802/aif.427

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     author = {Traynor, Tim},
     title = {Decomposition of group-valued additive set functions},
     journal = {Annales de l'Institut Fourier},
     pages = {131--140},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {22},
     number = {3},
     year = {1972},
     doi = {10.5802/aif.427},
     mrnumber = {48 #11439},
     zbl = {0228.28004},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.427/}
}

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Traynor, Tim. Decomposition of group-valued additive set functions. Annales de l'Institut Fourier, Volume 22 (1972) no. 3, pp. 131-140. doi : 10.5802/aif.427. http://www.numdam.org/articles/10.5802/aif.427/

References
Cited by

[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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