Copies of c0 in the space of Pettis integrable functions with integrals of finite variation
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- Ferrando, J.C. Acta Math Hung (2012) 135: 24. doi:10.1007/s10474-011-0158-3
Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. If all X-valued Pettis integrals defined on (Ω,Σ,μ) have separable ranges we show that the space of all weakly μ-measurable (classes of scalarly equivalent) X-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of c0 if and only if X does.