Lipschitz Function

from Encyclopedia of Mathematics

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