Proposition 3.87 . [02NC]

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Proposition 3.87.

Let $\|\cdot\|$ be any metric on $N_{\mathbb{R}}$ and $f\in{\overline{\mathscr{D}}}(N_{\mathbb{R}})$ . Then there exists a constant $\kappa>0$ such that, for all $u,v\in N_{\mathbb{R}}$ ,

|f(u)-f(v)|\leq\kappa\|u-v\|.