Let X be an infinite-dimensional Banach space. In 1995, settling a long
outstanding problem of Pettis, Dilworth and Girardi constructed an X-valued
Pettis integrable function on [0; 1] whose primitive is nowhere weakly
differentiable. Using their technique and some new ideas we show that ND, the
set of strongly measurable Pettis integrable functions with nowhere weakly
differentiable primitives, is lineable, i.e., there is an infinite dimensional
vector space whose nonzero vectors belong to ND
