Accepted Paper

Inserted: 11 jun 2024
Last Updated: 14 jan 2025

Journal: Nonlinear Analysis
Year: 2024

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.

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• UDS_in_Laakso_Space-2.pdf