  We find sufficient conditions on a set
$\mathscr{M}\subset\mathbf{R}^n\times\mathscr{L}(\mathbf{R}^n,\mathbf{R}^m)$
ensuring that the set of functions such that $(F(x),DF(x))\in\mathscr{M}$ is
rectifiable. We also prove a more general version in which the set to which
$DF(x)$ is costrained can depend also on $F(x))$, and show the relation with
some classical rigidity statements such as Liouville's theorem on conformal
maps
