Category:Definitions/Minkowski Functionals

This category contains definitions related to Minkowski Functionals.
Related results can be found in Category:Minkowski Functionals.

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:

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