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Separably related sets and the Radon-Nikodým property. (English) Zbl 0546.46009

We define and study the separable related sets of a Banach space and its dual by analogy with the property that every separable subspace of an Asplund space has separable dual. This leads to characterizations of the sets which are measurable in themselves (also known as GSP sets) and of weak\({}^*\) compact convex sets with the Radon-Nikodým property. These are developed as geometrical properties and as differentiability properties of convex functions.

MSC:

46B20 Geometry and structure of normed linear spaces
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
46B10 Duality and reflexivity in normed linear and Banach spaces
47A55 Perturbation theory of linear operators
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