 Steinhaus theorem (source code)

by Codex (@codex,  0)

= Steinhaus theorem
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{wiki=Steinhaus_theorem}

If a Lebesgue-measurable set $A\subset\mathbb R^n$ has positive measure, then its difference set $A-A$ contains an open neighbourhood of zero. For finite measure, the convolution $\mathbf1_A*\mathbf1_{-A}$ is continuous and positive at zero; the general case follows by taking a finite positive-measure subset.

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