Lineability of non-differentiable Pettis primitives

Let be an infinite-dimensional Banach space. In 1995, settling a long outstanding problem of Pettis, Dilworth and Girardi constructed an -valued Pettis integrable function on whose primitive is nowhere weakly differentiable. Using their technique and some new ideas we show that , 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 .