  We prove that if $u:\mathbb{R}^n\to\mathbb{R}$ is strongly convex, then for
every $\varepsilon>0$ there is a strongly convex function $v\in
C^2(\mathbb{R}^n)$ such that $|\{u\neq v\}|<\varepsilon$ and $\Vert
u-v\Vert_\infty<\varepsilon$.
