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This article is available for purchase or by subscription. See below.
Abstract
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Let E be a Banach space that is
complemented in its bidual by a projection P : E∗∗→ E. It is shown that E has
the Radon Nikodym property if and only if for every Radon probability
measure λ on the unit ball K of E∗∗ such that ω∗−∫
A x∗∗dλ ∈ E for every
weak∗ Borel subset A of K, the projection P is λ-Lusin measurable and
for every x∗ in E∗ the map x∗P satisfies the barycentric formula for λ on
K.
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Mathematical Subject Classification 2000
Primary: 46B22
Secondary: 28C15
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Milestones
Received: 25 April 1980
Published: 1 December 1981
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