Some characterizations of weak Radon-Nikodým sets
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- by Elias Saab PDF
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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 $(M,\sigma ({E^*},{E^{**}}))$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- 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