Universal Differentiability Sets in Laakso Space

2024/06/11 by Eriksson-Bique, Sylvester, Pinamonti, Andrea, Speight, Gareth
#46T20 #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2406.07660

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.

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