Minkowski Functional of Convex Absorbing Set is Sublinear Functional

Theorem

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

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

Let $A$ be a convex absorbing set.

Let $\mu_A$ be the Minkowski functional of $A$.

Then $\mu_A$ is a sublinear functional.

Proof

This follows from Minkowski Functional of Convex Absorbing Set is Positive Homogeneous and Minkowski Functional of Convex Absorbing Set is Sublinear.

$\blacksquare$