Geodesic
On the structure of universal differentiability sets
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 315-326.

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A subset of $\mathbb R^{d}$ is called a universal differentiability set if it contains a point of differentiability of every Lipschitz function $f\colon\mathbb R^{d}\to \mathbb R$. 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.
DOI : 10.14712/1213-7243.2015.218
Classification : 46G05, 46T20
Keywords: differentiability; Lipschitz functions; universal differentiability set; $\sigma$-porous set 
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Dymond, Michael. On the structure of universal differentiability sets. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 315-326. doi : 10.14712/1213-7243.2015.218. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.218/

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