First Borel class sets in Banach spaces and the asymptotic-norming property
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The Radon-Nikodým property in a separable Banach spaceX is related to the representation ofX as a weak* first Borel class subset of some dual Banach space (its bidualX**, for instance) by well known results due to Edgar and Wheeler , and Ghoussoub and Maurey [9, 10, 11]. The generalizations of those results depend on a new notion of Borel set of the first class “generated by convex sets” which is more suitable to deal with non-separable Banach spaces. The asymptotic-norming property, introduced by James and Ho , and the approximation by differences of convex continuous functions are also studied in this context.
KeywordsBanach Space Separable Banach Space Symmetric Convex Baire Space Pointwise Limit
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