On measurable projections in Banach spaces

Elias Saab

Vol. 97 (1981), No. 2, 453–459

DOI: 10.2140/pjm.1981.97.453

Abstract

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.

Mathematical Subject Classification 2000

Primary: 46B22

Secondary: 28C15

Milestones

Received: 25 April 1980

Published: 1 December 1981