 Minkowski functional

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 $U=\{x:p_U(x)<1\}$.

The Minkowski functional, often associated with convex analysis and geometry, is a generalization of the concept of a norm. It is defined within the context of a convex set in a vector space, particularly in relation to a symmetric convex body.