Universal Differentiability Sets in Laakso Space
Functional Analysis
2025-01-08 v2 Metric Geometry
Abstract
We show that there exists a family of mutually singular doubling measures on Laakso space with respect to which real-valued Lipschitz functions are almost everywhere differentiable. This implies that there exists a measure zero universal differentiability set in Laakso space. Additionally, we show that each of the measures constructed supports a Poincar\'e inequality.
Cite
@article{arxiv.2406.07660,
title = {Universal Differentiability Sets in Laakso Space},
author = {Sylvester Eriksson-Bique and Andrea Pinamonti and Gareth Speight},
journal= {arXiv preprint arXiv:2406.07660},
year = {2025}
}
Comments
arXiv admin note: text overlap with arXiv:2208.03361