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 set.

We define the Minkowski functional $\mu_A : X \to \closedint 0 \infty$ by:


 * $\map {\mu_A} x = \inf \set {t > 0 : t^{-1} x \in A}$

for each $x \in X$.

Also see

 * Minkowski Functional of Absorbing Set is Finite