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

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     title = {On vector measures},
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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://archive.numdam.org/articles/10.5802/aif.576/

[1] N. Dunford and J. T. Schwartz, Linear operators Part. I., Interscience Publishers Inc., New York, 1958. | Zbl

[2] J. Hoffmann-Jørgensen, Vector measures, Math. Scand., 28 (1971), 5-32. | Zbl

[3] J. Labuda, Sur quelques généralisations des théorèmes de Nikodym et de Vitali-Hahn-Saks, Bull. Acad. Pol. Sci. Math., 20 (1972), 447-456. | MR | Zbl

[4] J. Labuda, Sur le théorème de Bartle-Dunford-Schwartz, Bull. Acad. Pol. Sci. Math., 20 (1972), 549-553. | MR | Zbl

[5] D. Landers and L. Rogge, The Hahn-Vitali-Saks and the uniform boundedness theorem in topological groups, Manuscripta Math., 4 (1971), 351-359. | MR | Zbl

[6] A. P. Robertson, Unconditional convergence and the Vitali-Hahn-Saks theorem, Bull. Soc. Math. France, Mémoire 31-32 (1972), 335-341. | Numdam | MR | Zbl

[7] E. Thomas, L'intégration par rapport à une mesure de Radon vectorielle, Ann. Inst. Fourier 20, 2 (1970), 55-191. | Numdam | MR | Zbl

[8] I. Tweddle, Vector-valued measures, Proc. London Math. Soc., 20 (1970), 469-485. | MR | Zbl

[9] L. Drewnowski, On control submeasures anal measures, Studia Math., 50 (1974), 203-224. | MR | Zbl

[10] K. Musiak, Absolute continuity of vector measures, Coll. Math., 27 (1973), 319-321. | MR | Zbl

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