Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am looking for a proof of the Radon–Nikodým theorem in the case of vector valued measures. Many textbooks cover the scalar case. The book I am reading mentions the vector valued case but does not provide a proof or a reference. Any help is greatly appreciated.

Thanks, Phanindra.

share|cite|improve this question
One standard reference is Diestel-Uhl. – t.b. Nov 2 '11 at 3:35

The Radon-Nikodym theorem is false in general for Banach valued measures. Banach spaces for which the RN theorem theorem holds are said to have RNP (Radon-Nikodym Property). For example, Hilbert spaces, reflexive space. On the other hand, $L^1$ does not have RNP. You may check the Wikipedia article.

share|cite|improve this answer

Radon Nikodym theorem holds for Hilbert valued measures. A proof can be found in analysis II Serge Lang Addison Welsly 1968 or Real and functional analysis 3rd edition serge lang springer verlag 1993. There it is stated that a version of Radon Nikodym theprem can hold for banach spaces if one makes appropriate definitions and the relevant research paper is cited.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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