Hölder continuity and differentiability on subsequences

Details Hölder continuity and differentiability on subsequences Hölder continuity and differentiability on subsequences

2011-08-08

arxiv.org/abs/1108.1756v1

Mathematics

Classical Analysis and ODEs

Scientific paper

It is shown that an arbitrary function from $D\subset \R^n$ to $\R^m$ will
become $C^{0,\alpha}$-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 H\"older exponent $\alpha=\min\{1,\frac{n}{m}\}$ is
optimal.

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