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Testing on null sequences is enough for Bochner integrability

Published online by Cambridge University Press:  17 April 2009

Fernando Mayoral  and
Pedro J. Paúl
Pedro J. Paúl
Affiliation:
E.S. Ingenieros Industriales, Avda. Reina Mercedes s/n, 41012–Sevilla, Spain email: [email protected]
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Abstract

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Let E be a normed space, a Fréchet space or a complete (DF)-space satisfying the dual density condition. Let Ω be a Radon measure space. We prove that a function f: Ω → Eis Bochner p-integrable if (and only if) fis p-integrable with respect to the topology of uniform convergence on the norm-null sequences from E′.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 299 - 307
Copyright
Copyright © Australian Mathematical Society 1996

References

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