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On the Radon-Nikodým theorem and locally convex spaces with the Radon-Nikodým property

1977
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Proceedings of the American Mathematical Society
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Let F be a quasi-complete locally convex space, (fi, 2, ¡i) a complete probability space, and L\¡i; F) the space of all strongly integrable functions /: Ü -> F with the Egoroff property. If F is a Banach space, then the Radon-Nikodym theorem was proved by Rieffel. This result extends to Freenet spaces. If F is dual nuclear, then the Lebesgue-Nikodym theorem for the strong integral has been established. However, for nonmetrizable, or nondual nuclear spaces, the Radon-Nikodym theorem is not

doi:10.1090/s0002-9939-1977-0435338-2
fatcat:gwdk34pierbvfghrnolnvbjhgu