A compact null set containing a differentiability point of every Lipschitz function

TL;DR

The paper constructs an explicit compact null set in Euclidean space of dimension at least two, ensuring every Lipschitz function is differentiable at some point within this set.

Contribution

It introduces a novel explicit construction of a null set that guarantees differentiability points for all Lipschitz functions in higher dimensions.

Findings

Existence of a compact measure-zero set with universal differentiability property

Explicit construction of such a set in Euclidean space

Ensures differentiability of all Lipschitz functions at some point in the set

Abstract

We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly.