Minkowski functional (source code)

= Minkowski functional
{wiki}

For an absorbing convex set $U$ containing zero, its Minkowski functional is $p_U(x)=\inf\{t>0:x\in tU\}$. If $U$ is open and convex, then $p_U$ is sublinear and $U=\{x:p_U(x)<1\}$.