A characterization of strongly measurable Pettis integrable functions
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- by J. J. Uhl PDF
- Proc. Amer. Math. Soc. 34 (1972), 425-427 Request permission
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 ${x^ \ast } \in {\mathfrak {X}^ \ast }$.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- 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