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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of strongly measurable Pettis integrable functions


Author: J. J. Uhl
Journal: Proc. Amer. Math. Soc. 34 (1972), 425-427
MSC: Primary 28A45
DOI: https://doi.org/10.1090/S0002-9939-1972-0316675-4
MathSciNet review: 0316675
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Abstract: Let $ \mathfrak{X}$ be a Banach space and $ (\Omega ,\Sigma ,\mu )$ be a finite measure space. A strongly measurable $ f:\Omega \to \mathfrak{X}$ is Pettis integrable if and only if there exists a Young's function $ \Phi $ with $ {\lim _{t \to \infty }}\Phi (t)/t = \infty $ such that $ {x^ \ast }f \in {L^\Phi }(\mu )$ for all $ {x^ \ast } \in {\mathfrak{X}^ \ast }$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0316675-4
Article copyright: © Copyright 1972 American Mathematical Society