Let $T$ be a distribution with compact support and $T\lambda$ be a regularizing sequence of $T$. If we define for each $\lambda>0$, $M_\lambda(\eta)=\sup_\xi|\hat T_\lambda(\xi+i\eta)|$, $\eta\in\mathbb R^n$ then $H(\eta)=\lim_{\lambda\to0}\lim_{t\to0}\frac{\log M_\lambda(t\eta)-\log M_\lambda(0)}t$ is the supporting function of the smallest compact convex set supporting $T$.