Definition:Lipschitz Equivalence/Metrics

Metric Spaces
Let $A$ be a set upon which there are two metrics imposed: $d$ and $d\,'$.

Let $\exists h, k \in \R_{>0}$ such that:
 * $\forall x, y \in A: h d\,' \left({x, y}\right) \le d \left({x, y}\right) \le k d\,' \left({x, y}\right)$

Then $d$ and $d\,'$ are described as Lipschitz equivalent.

Terminology
Despite the close connection with the concept of Lipschitz continuity, this concept is rarely seen in mainstream mathematics, and appears not to have a well-established name.

The name Lipschitz equivalence appears in :
 * There does not appear to be a standard name for this; the name we use is reasonably appropriate ...

Also see

 * Lipschitz Equivalence is Equivalence Relation


 * Lipschitz Continuity