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Testing on null sequences is enough for Bochner integrability
Published online by Cambridge University Press: 17 April 2009
Abstract
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