Nowhere Weak Differentiability of the Pettis Integral
  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. 
Stephen J. Dilworth, Maria Girardi