Lipschitz Continuity

Considering the general case of $f:\mathcal{D}\to {\mathbb{R}}^m$ where $\mathcal{D}\subset {\mathbb{R}}^n$.

The function $f$ is said to be Lipschitz continuous on some set $\mathcal{N}\subset \mathcal{D}$ if there is a constant $L>0$ such that

$$||f(x_1)-f(x_0)||\le L||x_1-x_0||,\forall x_0,x_1\in \mathcal{N}$$

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Common Vector Norms (p-norms)