Minkowski functional

Summary

The Minkowski functional, or gauge, of an absorbing set $K$ in a vector space is a function on the space. Its value at $x$ is the smallest factor by which $K$ must be scaled to contain $x$. For convex sets it is sublinear, and for convex balanced sets it is a seminorm. It is the bridge between convex neighbourhoods of $0$ and seminorms, and so it is the main tool for describing locally convex spaces by seminorms.