Minkowski functional

Let X be a normed space and let K an absorbingPlanetmathPlanetmath convex subset of X such that 0 is in the interior of K. Then the Minkowski functional ρ:X is defined as


We put ρ(x)=0 whenever x=0. Clearly ρ(x)0 for all x.

It is important to note that in general ρ(x)ρ(-x).

is positively 1- homogeneousPlanetmathPlanetmathPlanetmath. This means that


for s>0.

Title Minkowski functional
Canonical name MinkowskiFunctional
Date of creation 2013-03-22 14:50:44
Last modified on 2013-03-22 14:50:44
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 18
Author Mathprof (13753)
Entry type Definition
Classification msc 46B20