Remark 1
Tag 07G1, permanent. Cite it as [Bourbaki, Tag 07G1].
Topological Vector Spaces, II, p. 40, § 5. Separation of convex sets
It follows from prop. 5 that is the upper envelope of a directed increasing family of functions that are the restrictions to of functions which are continuous and convex in .
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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