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 $\sigma(L^1,L^\infty)$.

  • 3
    $\begingroup$ The book of Albiac and Kalton. $\endgroup$ – Bill Johnson Aug 29 '14 at 17:06
  • $\begingroup$ 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. $\endgroup$ – 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.


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.