Porous sets that are Haar null, and nowhere approximately differentiable functions

We define a new notion of "HP-small" set A which implies that A is both sig ma -porous and Haar null in the sense of Christensen. We show that the set of all continuous functions on [0, 1] which have finite unilateral approxim ate derivative at a point x is an element of [0, 1] is HP-small, as well as its projections onto hyperplanes. As a corollary, the same is true for the set of all Besicovitch functions. Also, the set of continuous functions on [0, 1] which are Holder at a point is HP-small.