A Geometrical Characterization of Banach Spaces with the Radon-Nikodym Property
A Geometrical Characterization of Banach Spaces with the Radon-Nikodym Property
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 …