Minkowski functional
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Let X be a vector space (possibly infinite dimensional), and let K be an absorbing convex subset of X. The Minkowski functional p of K is defined on X by the mapping 
,
.
It can be shown that the Minkowski functional satisfies the following properties:
1. 
for all 
.
2. Homogeneity: p(αx) = αp(x) for all α > 0.
3. Subadditivity: 
.
[edit] Normed spaces
Minkowski functionals are often used in the study of normed spaces. For example, if X is a normed space and K is the unit sphere on X, 
is just the norm on X. In a normed space, the Minkowski functional of a convex absorbing set satisfies the following additional properties
1. p is continuous.
2. closure(K) = 
.
3. interior(K) = 
.
