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arXiv · 1607.05933

On the structure of universal differentiability sets

Michael Dymond
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Abstract

We prove that universal differentiability sets in Euclidean spaces possess distinctive structural properties. Namely, we show that any universal differentiability set contains a `kernel' in which the points of differentiability of each Lipschitz function are dense. We further prove that no universal differentiability set may be decomposed as a countable union of relatively closed, non-universal differentiability sets. The sharpness of this result, with respect to existing decomposibility results of the opposite nature, is discussed.

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Michael Dymond. 2016-07-20. On the structure of universal differentiability sets. https://arxiv.org/abs/1607.05933

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