A relation between finitary Lipschitz extension moduli

TL;DR

This paper establishes a simple relationship between Lipschitz extension moduli for finite point sets and the entire space, enabling improved bounds by leveraging existing literature.

Contribution

It provides an elementary bound connecting Lipschitz extension moduli for finite and infinite sets, facilitating the application of known results to new problems.

Findings

Bound on Lipschitz extension modulus for n points in terms of the modulus for the entire space

Enables improved bounds by referencing existing literature

Simplifies the analysis of Lipschitz extensions in metric spaces

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.