2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152933For 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.Functional Analysis46Etext