Theorem 4
Tag 07Y3, permanent. Cite it as [Bourbaki, Tag 07Y3].
Topological Vector Spaces, chapter V, § 1. Prehilbertian spaces and hilbertian spaces
In a hilbertian space E, the unit ball is weakly compact.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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