Vol. 97, No. 2, 1981

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On measurable projections in Banach spaces

Elias Saab

Vol. 97 (1981), No. 2, 453–459

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∗∗E for every weak Borel subset A of K, the projection P is λ-Lusin measurable and for every x in E the map xP satisfies the barycentric formula for λ on K.

Mathematical Subject Classification 2000
Primary: 46B22
Secondary: 28C15
Received: 25 April 1980
Published: 1 December 1981
Elias Saab