Doubling Metric Spaces are Characterized by a Lemma of Benjamini and Schramm

TL;DR

This paper reveals that a property of Euclidean space, identified by Benjamini and Schramm, actually characterizes all doubling metric spaces, providing a new perspective on their structure.

Contribution

It demonstrates that a key property of Euclidean space can be used to characterize doubling metric spaces, linking Euclidean and more general metric space properties.

Findings

Doubling metric spaces are characterized by a property originally observed in Euclidean space.

The property of Euclidean space by Benjamini and Schramm applies to all doubling metric spaces.

This characterization offers new insights into the structure of doubling metric spaces.

Abstract

A useful property of Euclidean space originally shown by I. Benjamini and O. Schramm turns out to characterize doubling metric spaces.