Universal Differentiability Sets in Laakso Space (2406.07660v2)

Published 11 Jun 2024 in math.FA and math.MG

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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