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Norm-closed convex set is weakly closed

A norm-closed convex subset of a Banach space contains every weak limit of its sequences. Apply Mazur lemma to obtain norm-convergent convex combinations that remain in the set.

Ancestors (7)

  1. Weak convergence in a Hilbert space
  2. Hilbert space
  3. Functional analysis
  4. Analysis
  5. Area of mathematics
  6. Mathematics
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