Remark 4
Tag 07J1, permanent. Cite it as [Bourbaki, Tag 07J1].
Topological Vector Spaces, II, p. 56, § 7. Extremal points and extremal generators
If A is a compact convex set in a Hausdorff locally convex space, it may happen that an extremal point of A does not belong to any support hyperplane of A (II, p. 78, exerc. 11). The proof of theorem 1 (II, p. 56) shows that in any case A is the convex closed envelope of the set of extremal points of A which belong to a support hyperplane.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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