Geodesic
An Analog of the Krein–Mil'man Theorem for Strongly Convex Hulls in Hilbert Space
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 37-42 
M. V. Balashov. An Analog of the Krein–Mil'man Theorem for Strongly Convex Hulls in Hilbert Space. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 37-42. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a3/
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     author = {M. V. Balashov},
     title = {An {Analog} of the {Krein{\textendash}Mil'man} {Theorem} for {Strongly} {Convex} {Hulls} in {Hilbert} {Space}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the following theorem: in Hilbert space a closed bounded set is contained in the strongly convex $R$-hull of its $R$-strong extreme points. $R$-strong extreme points are a subset of the set of extreme points (it may happen that these two sets do not coincide); the strongly convex $R$-hull of a set contains the closure of the convex hull of the set.

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