Geodesic
Note on Pointwise Convergence on the Choquet Boundary
Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 109-113

Voir la notice de l'article provenant de la source Cambridge University Press

In [6] J. Rainwater obtained the following theorem.Theorem. Let N be a normed linear space, {xn} a bounded sequence of elements in N and X ∊ N. for each extreme point f of the unit ball of N✶, then {xn} converges weakly to x.Now let X be a compact Hausdorff space and H a linear subspace of C(X) (all real-valued continuous functions on X ) which separates the points of X and contains the constant functions. If x∊X, then MX(H) denotes the set of positive linear functionals μ on C(X) such that μ(h) = h(x) for all h in H. 
Grossman, Marvin W. Note on Pointwise Convergence on the Choquet Boundary. Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 109-113. doi: 10.4153/CMB-1967-012-6
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[1] 1. Bauer, H., Silovscher Rand und Dirichletsches Problem. Ann. Inst. Fourie. (Grenoble) 11 (1966), pages 89-136. Google Scholar | DOI

[2] 2. Bishop, E. and de Leeuw, K., The representation of linear functionals by measures on sets of extreme points. Ann. Inst. Fourie. (Grenoble) 9 (1955), pages 305-331. Google Scholar | DOI

[3] 3. Day, M. M., Normed Linear Spaces. Springer-Verlag, Berlin (1955). Google Scholar

[4] 4. Phelps, R. R., Lectures on Choquet's Theorem. D. Van Nostrand, Princeton (1966). Google Scholar

[5] 5. Pták, V., A combinatorial lemma on the existence of convex means and its applications to weak compactness. Proc. of Symposia in Pure Mathematics. Vol. 7, Convexity, Amer, Math. Soc. (1966), pages 211-219. Google Scholar

[6] 6. Rainwater, J., Weak convergence of bounded sequences. Proc. Amer. Math. Soc. 6 (1966), page 999. Google Scholar

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