In mathematics, Mazur's lemma is a result in the theory of normed vector spaces introduced by Polish mathematician Stanisław Mazur. 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. Mazur's lemma is used in the proof of Tonelli's theorem.
Statement of the lemma
For a proof see Ekeland & Temam (1974), p. 6.
See also
References