On vector measures
Annales de l'Institut Fourier, Tome 25 (1975) no. 3-4, pp. 139-161.

Soit l’espace de Banach des mesures réelles sur une tribu R, son dual, E un espace localement convexe quasi-complet, E son dual et μ une mesure sur R à valeurs dans E. On démontre que pour chaque θ il existe un élément θdμE tel que x μ,θ= θ d μ , x pour tout x E . Si (θ i ) iI est une famille filtrante décroissante dans , dont l’infimum est 0, alors le filtre des sections de θ i d μ i I converge vers 0.

Let be the Banach space of real measures on a σ-ring R, let be its dual, let E be a quasi-complete locally convex space, let E be its dual, and let μ be an E-valued measure on R. If is shown that for any θ there exists an element θdμ of E such that x μ,θ= θ d μ , x for any x E and that the map

θ θ d μ : E

is order continuous. It follows that the closed convex hull of μ(R) is weakly compact.

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     title = {On vector measures},
     journal = {Annales de l'Institut Fourier},
     pages = {139--161},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {25},
     number = {3-4},
     year = {1975},
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     url = {http://www.numdam.org/articles/10.5802/aif.576/}
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Constantinescu, Corneliu. On vector measures. Annales de l'Institut Fourier, Tome 25 (1975) no. 3-4, pp. 139-161. doi : 10.5802/aif.576. http://www.numdam.org/articles/10.5802/aif.576/

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