Let $v$ be any convex function on $B_{1}\subset\mathbb{R}^{n}$ with sections $S_{h,p}^{v}$, and let $\Sigma_{v}$ denote the set of points $x$ such that for all supporting slopes $p$ at $x$, there is some $C_{p}$ such that

$$|S_{h,p}^{v}(x)|<C_{p}h^{\frac{n+1}{2}}$$

for all $h$ small. Then

$$\mathcal{H}^{n-1}(\Sigma_{v})=0.$$