  We consider Carleson's problem regarding pointwise convergence for the
Schr\"odinger equation. Bourgain recently proved that there is initial data, in
$H^s(\mathbb{R}^n)$ with $s<\frac{n}{2(n+1)}$, for which the solution diverges
on a set of nonzero Lebesgue measure. We provide a different example enabling
the generalisation to fractional Hausdorff measure.
