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Some characterizations of weak Radon-Nikodým sets


Author: Elias Saab
Journal: Proc. Amer. Math. Soc. 86 (1982), 307-311
MSC: Primary 46B22; Secondary 46G10
DOI: https://doi.org/10.1090/S0002-9939-1982-0667295-X
MathSciNet review: 667295
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Abstract: Let $ K$ be a weak*-compact convex subset of the dual $ {E^*}$ of a Banach space $ E$. It is shown that $ K$ has the weak Radon-Nikodym property if and only if every $ {x^{**}}$ in $ {E^{**}}$ restricted to $ K$ is universally measurable if and only if every $ {x^{**}}$ in $ {E^{**}}$ restricted to any weak*-compact subset $ M$ of $ K$ has a point of continuity on ($ M$, weak*) if and only if $ K$ is a set of complete continuity if and only if every subset of $ K$ is weak* dentable in $ (M,\sigma ({E^*},{E^{**}}))$.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0667295-X
Keywords: (Weak) Radon-Nikodym, sets of complete continuity
Article copyright: © Copyright 1982 American Mathematical Society

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