NOWHERE WEAK DIFFERENTIABILITY OF THE PETTIS INTEGRAL
Authors:
- 1 October 1995
- journal article
- research article
- Published by Taylor & Francis in Quaestiones Mathematicae
- Vol. 18  (4) , 365-380
Abstract
For an arbitrary infinite-dimensional Banach space đť”›, we construct examples of strongly-measurable đť”›-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 nondifferentia-bility of the indefinite Pettis integral to the cotype of đť”›, from which it follows that our examples are reasonably sharp.Keywords
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