A relation between finitary Lipschitz extension moduli

Abstract

This short note contains an elementary observation in response to the recent posting arXiv:1707.06593v1, which studies the Lipschitz extension modulus to $n$ additional points. We bound this modulus in terms of the well-studied Lipschitz extension modulus from $n$ points to the entire ambient metric space, thus making it possible to quote the available literature to improve some of the bounds obtained in arXiv:1707.06593v1.