Definition:Lipschitz Equivalence/Metrics/Definition 1

Definition
Let $M_1 = \struct {A, d_1}$ and $M_2 = \struct {A, d_2}$ be metric spaces on the same underlying set $A$.

Let $\exists h, k \in \R_{>0}$ such that:
 * $\forall x, y \in A: h \map {d_2} {x, y} \le \map {d_1} {x, y} \le k \map {d_2} {x, y}$

Then $d_1$ and $d_2$ are described as Lipschitz equivalent.

Also see

 * Equivalence of Definitions of Lipschitz Equivalent Metrics