Definition:Lipschitz Equivalence/Metrics/Definition 2

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

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

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

Also see

 * Equivalence of Definitions of Lipschitz Equivalent Metrics