A compact universal differentiability set with Hausdorff dimension one

TL;DR

This paper presents a concise proof that in any non-zero Euclidean space, there exists a compact set of Hausdorff dimension one that contains a differentiability point for every Lipschitz function, highlighting a universal differentiability property.

Contribution

It provides a short, elegant proof of the existence of a universal differentiability set with Hausdorff dimension one in Euclidean spaces.

Findings

Existence of a compact universal differentiability set of Hausdorff dimension one

Universal differentiability points are contained in a small, structured set

The proof simplifies previous constructions of such sets

Abstract

We give a short proof that any non-zero Euclidean space has a compact subset of Hausdorff dimension one that contains a differentiability point of every real-valued Lipschitz function defined on the space.