Mazur's lemma

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In mathematics, Mazur's lemma is a result in the theory of normed vector spaces. It shows that any weakly convergent sequence in a normed space has a sequence of convex combinations of its members that converges strongly to the same limit, and is used in the proof of Tonelli's theorem.

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Statement of the lemma

Mazur's theorem  Let be a normed vector space and let be a sequence converges weakly to some .

Then there exists a sequence made up of finite convex combination of the 's of the form

such that strongly that is .

See also

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