Abstract
We prove that in a Euclidean space of dimension at least two, there exists a compact set of Lebesgue measure zero such that any real-valued Lipschitz function defined on the space is differentiable at some point in the set. Such a set is constructed explicitly.
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The authors acknowledge support of EPSRC grant EP/D053099/1.
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Doré, M., Maleva, O. A compact null set containing a differentiability point of every Lipschitz function. Math. Ann. 351, 633–663 (2011). https://doi.org/10.1007/s00208-010-0613-4
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DOI: https://doi.org/10.1007/s00208-010-0613-4