A geometrical characterization of Banach spaces with the Radon-Nikodym property

Maynard, Hugh B.

doi:10.1090/S0002-9947-1973-0385521-0

A geometrical characterization of Banach spaces with the Radon-Nikodym property
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by Hugh B. Maynard PDF

Trans. Amer. Math. Soc. 185 (1973), 493-500 Request permission

Abstract:

A characterization of Banach spaces having the Radon-Nikodym property is obtained in terms of a convexity requirement on all bounded subsets. In addition a Radon-Nikodym theorem, utilizing this convexity property, is given for the Bochner integral and it is easily shown that this theorem is equivalent to the Phillips-Metivier Radon-Nikodym theorem as well as all the standard Radon-Nikodym theorems for the Bochner integral.

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