Definition:Minkowski Functional

Definition
Let $\GF \in \set {\R, \C}$.

Let $X$ be a vector space over $\GF$.

Let $A \subseteq X$ be a convex absorbing subset of $X$.

The Minkowski functional of $A$ is the real-valued function $\mu_A : X \to \closedint 0 \infty$ defined as:


 * $\forall x \in X: \map {\mu_A} x = \inf \set {t > 0 : \dfrac x t \in A}$

Also see

 * Minkowski Functional of Absorbing Set is Finite