Definition:Lipschitz Equivalence/Metrics/Definition 2

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 $\exists K_1, K_2 \in \R_{>0}$ such that:
 * $(1): \quad \forall x, y \in A: \map {d_2} {x, y} \le K_1 \map {d_1} {x, y}$
 * $(2): \quad \forall x, y \in A: \map {d_1} {x, y} \le K_2 \map {d_2} {x, y}$

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

Also see

 * Equivalence of Definitions of Lipschitz Equivalent Metrics