\begin{definition}[Definition:Minkowski Functional]
Let $E$ be a vector space over $\R$.
A functional $p: E \to \R$ is called a '''Minkowski functional''' {{{iff}} it satisfies:
{{begin-axiom}}
{{axiom | n = 1
        | q = \forall x \in E, \forall \lambda \in \R_{>0}
        | ml= \map p {\lambda x}
        | mo= =
        | mr= \lambda \map p x
        | rc= that is, $p$ is positive homogeneous
}}
{{axiom | n = 2
        | q = \forall x, y \in E
        | ml= \map p {x + y}
        | mo= \le
        | mr= \map p x + \map p y
        | rc= that is, $p$ is sub-additive
}}
{{end-axiom}}
{{NamedforDef|Hermann Minkowski|cat = Minkowski}}
Category:Definitions/Functional Analysis
Category:Definitions/Topology
\end{definition}