Lipschitz function

Let function $f:[a,b]\to \mathbb R$ such that for some constant M and for all $x,y\in [a,b]$ \begin{equation}\label{eq:1} |f(x)-f(y)| \leq M|x-y|. \end{equation} Then function $f$ is called Lipschitz on $[a,b]$ or one writes $f\in \operatorname{Lip}_M[a,b]$.