The McShane integral in weakly compactly generated spaces ✩

Di Piazza and Preiss asked whether every Pettis integrable function defined on [0, 1] and taking values in a weakly compactly generated Banach space is McShane integrable. In this paper we answer this question in the negative. Moreover, we give a counterexample where the target Banach space is reflexive. © 2010 Elsevier Inc. All rights reserved.