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

Soit ℳ l’espace de Banach des mesures réelles sur une tribu R, ℳ ′ 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∈ℳ ′ il existe un élément ∫θdμ∈E tel que 〈x ′ ∘μ,θ〉=∫ θ d μ , x ′ pour tout x ′ ∈E ′ . Si (θ i ) i∈I est une famille filtrante décroissante dans ℳ ′ , dont l’infimum est 0, alors le filtre des sections de ∫ θ i d μ ∣ i ∈ I converge vers 0.

Let ℳ be the Banach space of real measures on a σ-ring R, let ℳ ′ 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∈ℳ ′ 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→∫θdμ:ℳ′→E

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

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     author = {Constantinescu, Corneliu},
     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},
     doi = {10.5802/aif.576},
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     mrnumber = {53 #6301},
     language = {en},
     url = {https://aif.centre-mersenne.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. https://aif.centre-mersenne.org/articles/10.5802/aif.576/

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