##  [Minkowski Functional](/minkowski-functional) 

  ##  [Minkowski Functional](https://puremath.quantumdictionary.io/minkowski-functional-0) 

  

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Definition

Given a convex set K containing the origin, the Minkowski functional (gauge) p_K(x) is defined as the infimum of λ>0 such that x∈λK; it measures the scalar dilation required to bring a vector into K and generalizes the notion of a norm when K is balanced and absorbing.