On the representation of certain functionals by measures on the Choquet boundary
Annales de l'Institut Fourier, Volume 13 (1963) no. 1, pp. 111-121.

On utilise le théorème de Hahn-Banach pour construire quelques fonctionnelles sur des espaces de fonctions continues. On caractérise la frontière de Choquet, et on donne des démonstrations simples :

a) du théorème de Bishop et de Leeuw avec des conditions de séparabilité ;

b) du théorème de Bauer.

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     title = {On the representation of certain functionals by measures on the {Choquet} boundary},
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Edwards, David Albert. On the representation of certain functionals by measures on the Choquet boundary. Annales de l'Institut Fourier, Volume 13 (1963) no. 1, pp. 111-121. doi : 10.5802/aif.133. http://www.numdam.org/articles/10.5802/aif.133/

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[2] H. Bauer, Minimalstellen von Funktionen und Extremalpunkte II, Arch der Math., vol. 11, 1960, pp. 200-205. | MR | Zbl

[3] H. Bauer, Šilvscher Rand und Dirichletsches Problem, Ann. Inst. Fourier, Grenoble, vol. 11, 1961, pp. 89-136. | Numdam | MR | Zbl

[4] E. Bishop and K. De Leeuw, The representations of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier, Grenoble, vol. 9, 1959, pp. 305-331. | Numdam | MR | Zbl

[5] F. F. Bonsall, On the representation of the points of a convex set Journal London Math. Soc. (to appear). | Zbl

[6] M. Hervé, Sur les représentations intégrales à l'aide des points extremaux dans un ensemble compact convexe métrizable, C. R. Acad. Sci., Paris, vol. 253, 1961, pp. 366-368. | MR | Zbl

[7] R. V. Kadison, A representation theory for commutative topological algebra, Mem. Amer. Math. Soc., number 7, 1951, pp. 39. | MR | Zbl

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