Category:Minkowski Functionals
Jump to navigation
Jump to search
This category contains results about Minkowski Functionals.
Definitions specific to this category can be found in Definitions/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:
- $\forall x \in X: \map {\mu_A} x = \inf \set {t > 0 : \dfrac x t \in A}$
Subcategories
This category has only the following subcategory.
M
Pages in category "Minkowski Functionals"
The following 9 pages are in this category, out of 9 total.
M
- Minkowski Functional of Balanced Convex Absorbing Set in Vector Space is Seminorm
- Minkowski Functional of Convex Absorbing Set is Finite
- Minkowski Functional of Convex Absorbing Set is Positive Homogeneous
- Minkowski Functional of Convex Absorbing Set is Sublinear
- Minkowski Functional of Convex Absorbing Set is Sublinear Functional
- Minkowski Functional of Open Ball with respect to Seminorm is Seminorm
- Minkowski Functional of Open Convex Set containing Zero Vector in Topological Vector Space recovers Set
- Minkowski Functional of Symmetric Convex Absorbing Set in Real Vector Space is Seminorm