Abstract
We give a partial answer to the question in the title by showing that the McShane and Pettis integrals coincide for functions with values in super-reflexive spaces as well as for functions with values in $c_0(\Gamma)$. We also improve an example of Fremlin and Mendoza, according to which these integrals do not coincide in general, by showing that, at least under the Continuum Hypothesis, there is a scalarly negligible function which is not McShane integrable.
Citation
L. Di Piazza. D. Preiss. "When do McShane and Pettis integrals coincide?." Illinois J. Math. 47 (4) 1177 - 1187, Winter 2003. https://doi.org/10.1215/ijm/1258138098
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