Group Norm Metric

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A Group Norm Metric is a distance metric on a group ([math]\displaystyle{ G, +, 0 }[/math]), defined by [math]\displaystyle{ \mid\mid x + (-y)\mid\mid= \mid\mid x - y \mid\mid }[/math], where [math]\displaystyle{ \mid\mid . \mid\mid }[/math] is a group norm on G, i.e., a function [math]\displaystyle{ \mid\mid . \mid\mid: G \rightarrow \mathbb{R} }[/math] such that, for all [math]\displaystyle{ x, y \in G }[/math] we have the following properties ...



References

2006