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Pettis decomposition for universally scalarly measurable functions


Author: Elizabeth M. Bator
Journal: Proc. Amer. Math. Soc. 104 (1988), 795-800
MSC: Primary 28B05; Secondary 46G10
DOI: https://doi.org/10.1090/S0002-9939-1988-0964859-6
MathSciNet review: 964859
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Abstract: It is shown that if $ K$ is a compact Hausdorff space, $ X$ is a Banach space, and $ f:K \to {X^ * }$ is bounded and universally scalarly measurable, then $ f$ is $ \mu $-Pettis decomposable for every Radon measure $ \mu $ on $ K$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0964859-6
Keywords: Banach space, Pettis integral, universally scalarly measurable, Bourgain property
Article copyright: © Copyright 1988 American Mathematical Society

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