Nowhere Weak Differentiability of the Pettis Integral

Details Nowhere Weak Differentiability of the Pettis Integral Nowhere Weak Differentiability of the Pettis Integral

1994-10-31

arxiv.org/abs/math/9410203v1

Mathematics

Functional Analysis

Scientific paper

For 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.

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