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arXiv · 1805.01710

Steinhaus-type property for a boundary of a convex body

Wojciech Jablonski
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Abstract

We show that if $U\subset\partial A$ is a neighbourhood of a point $x_0\in\partial A$ of the boundary of a convex body $A$ then it has the so-called Stainhaus-type property (the interior of $(U+U)$ is nonempty) if and only if $x_0$ is not a point of flatness of the boundary~$\partial A$. This implies that additive functions as well as mid-convex functions, bounded above on~$U$, are continuous.

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BibTeXRIS

Wojciech Jablonski. 2018-05-04. Steinhaus-type property for a boundary of a convex body. https://arxiv.org/abs/1805.01710

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