  In this paper we prove that every collection of measurable functions
$f_\alpha$, $|\alpha|=m$ coincides a.e. with $m$th order derivatives of a
function $g\in C^{m-1}$ whose derivatives of order $m-1$ may have any modulus
of continuity weaker than that of a Lipschitz function. This is a stronger
version of earlier results of Lusin, Moonens-Pfeffer and Francos. As an
application we construct surfaces in the Heisenberg group with tangent spaces
being horizontal a.e.
