Universal Differentiability Sets in Laakso Space

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 Poincaré inequality.

arXiv admin note: text overlap with arXiv:2208.03361