# Proof of the Dunford-Pettis theorem

I would like to know where to find a complete proof of the Dunford-Pettis theorem: A sequence $(f_n)_{n\geq 0} \subset L^1$ is uniformly integrable if and only if it is relatively compact for the weak topology $\sigma(L^1,L^\infty)$.

• The book of Albiac and Kalton. – Bill Johnson Aug 29 '14 at 17:06
• You can also find it in the article by J. Diestel, Uniform integrability: an introduction. I believe you can freely access this on the web. – user19038 Aug 29 '14 at 22:40

This is surely in many places, but a reasonably complete proof is given in Section III.2, Theorem 15 of

J. Diestel, J. J. Uhl, Vector measures. American Mathematical Society 1977.