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

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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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     title = {Note on {Pointwise} {Convergence} on the {Choquet} {Boundary}},
     journal = {Canadian mathematical bulletin},
     pages = {109--113},
     year = {1967},
     volume = {10},
     number = {1},
     doi = {10.4153/CMB-1967-012-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-012-6/}
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