Mazur's lemma explained

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.

References

• Book: Renardy, Michael. Rogers, Robert C.. amp. An introduction to partial differential equations. Texts in Applied Mathematics 13. Second. Springer-Verlag. New York. 2004. 350. 0-387-00444-0.
• Book: Ekeland, Ivar. Temam, Roger. amp. Convex analysis and variational problems. Studies in Mathematics and its Applications, Vol. 1. Second. North-Holland Publishing Co., Amsterdam-Oxford, American. New York. 1976. 6.