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On Pettis integrability. (English) Zbl 1080.46515
Summary: Assuming that \((\Omega , \Sigma , \mu )\) is a complete probability space and \(X\) a Banach space, in this paper we investigate the problem of the \(X\)-inheritance of certain copies of \(c_0\) or \(\ell _{\infty }\) in the linear space of all [classes of] \(X\)-valued \(\mu \)-weakly measurable Pettis integrable functions equipped with the usual semivariation norm.

MSC:
46G10 Vector-valued measures and integration
28B05 Vector-valued set functions, measures and integrals
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