Given an input space $X$ and Metric $M$, a function $f: X \to \mathbb{R}$ on a Metric space $(X,M)$ is called a Lipschitz function, or Lipschitz continuous if there exists a constant $C_M$ such that $|f(x) - f(y)| \leq C_M M(x,y)$, for all $x,y \in X$.