# Typical differentiability within an exceptionally small set

## TL;DR

This paper constructs a special unrectifiable set where typical Lipschitz functions are mostly differentiable, challenging common assumptions about differentiability and rectifiability.

## Contribution

It introduces a new example of an unrectifiable set with large differentiability points for typical Lipschitz functions, expanding understanding of differentiability in geometric measure theory.

## Key findings

- Existence of a purely unrectifiable set with large differentiability points
- Construction based on Csörnyei, Preiss, and Tišer's universal differentiability set
- Challenges assumptions about differentiability on unrectifiable sets

## Abstract

We verify the existence of a purely unrectifiable set in which the typical Lipschitz function has a large set of full differentiability points. The example arises from a construction, due to Cs\"ornyei, Preiss and Ti\v{s}er, of a universal differentiability set in which a certain Lipschitz function has only a purely unrectifiable set of differentiability points.