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arXiv · 1108.1756

Hölder continuity and differentiability on subsequences

Volker Elling
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Abstract

It is shown that an arbitrary function from $D\subset \R^n$ to $\R^m$ will become $C^{0,α}$-continuous in almost every $x\in D$ after restriction to a certain subset with limit point $x$. For $n\geq m$ differentiability can be obtained. Examples show the Hölder exponent $α=\min\{1,\frac{n}{m}\}$ is optimal.

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Volker Elling. 2013-05-20. Hölder continuity and differentiability on subsequences. https://arxiv.org/abs/1108.1756

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