Krein-Šmulian theorem
= Krein-Šmulian theorem
{c}
{wiki=Krein–Smulian_theorem}
The closed convex hull of a weakly compact subset of a Banach space is weakly compact.
The other standard formulation says that a convex subset $C$ of a Banach-space dual is weak-star closed if its intersection with every norm-closed ball is weak-star closed.