# The Radon–Nikodým theorem for vector valued measures

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.

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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.