Nowhere Weak Differentiability of the Pettis Integral

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dc.creatorDilworth, Stephen J.
dc.creatorGirardi, Maria
dc.date1994-10-31
dc.date.accessioned2026-07-07T09:15:11Z
dc.date.available2026-07-07T09:15:11Z
dc.descriptionFor an arbitrary infinite-dimensional Banach space $\X$, we construct examples of strongly-measurable $\X$-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly differentiable; thus, for these functions the Lebesgue Differentiation Theorem fails rather spectacularly. We also relate the degree of nondifferentiability of the indefinite Pettis integral to the cotype of $\X$, from which it follows that our examples are reasonably sharp. This is an expanded version of a previously posted paper with the same name.
dc.identifierhttps://arxiv.org/abs/math/9410203
dc.identifierhttp://arxiv.org/abs/math/9410203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152933
dc.subjectFunctional Analysis
dc.subject46E
dc.titleNowhere Weak Differentiability of the Pettis Integral
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