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The McShane integral in weakly compactly generated spaces |
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| Authors: | A. Avilé s |
| Affiliation: | a Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30100 Espinardo (Murcia), Spain b Mathematical Institute, University of Wroc?aw, Pl. Grunwaldzki 2/4, 50-384 Wroc?aw, Poland c Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, 30100 Espinardo (Murcia), Spain |
| Abstract: | 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. |
| Keywords: | Pettis integral McShane integral Scalarly null function Filling family |
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