= Bounded Lipschitz norm
{title2=$\|f\|_{\rm BL}=\sup_{x\ne y}|f(x)-f(y)|/d(x,y)+\sup_z|f(z)|$}
The bounded Lipschitz norm combines the <Lipschitz constant> and <supremum norm> of a bounded real-valued <Lipschitz function> on a <metric space>. Both summands satisfy the <triangle inequality>; the supremum term makes the sum definite even on constant functions. Its unit ball requires the sum of the two bounds to be at most one, a stronger requirement than bounding each separately by one.
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