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

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

θθdμ:E

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

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.

@article{AIF_1975__25_3-4_139_0,
     author = {Constantinescu, Corneliu},
     title = {On vector measures},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {25},
     number = {3-4},
     year = {1975},
     pages = {139-161},
     doi = {10.5802/aif.576},
     zbl = {0286.46044},
     mrnumber = {53 \#6301},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1975__25_3-4_139_0}
}
Constantinescu, Corneliu. On vector measures. Annales de l'Institut Fourier, Volume 25 (1975) no. 3-4, pp. 139-161. doi : 10.5802/aif.576. http://www.numdam.org/item/AIF_1975__25_3-4_139_0/

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