McShane extension theorem
= McShane extension theorem
{c}
{wiki}
If $f:A\to\mathbb R$ is $L$-Lipschitz on a subset of a metric space, then
$$
F(x)=\inf_{y\in A}\{f(y)+Ld(x,y)\}
$$
extends $f$ to the whole space and remains $L$-Lipschitz.
= McShane extension theorem
{c}
{wiki}
If $f:A\to\mathbb R$ is $L$-Lipschitz on a subset of a metric space, then
$$
F(x)=\inf_{y\in A}\{f(y)+Ld(x,y)\}
$$
extends $f$ to the whole space and remains $L$-Lipschitz.