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Reid Barton
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Name for an inequality of isoperimetric type

I want to know if the following fact has a standard name and/or reference

Let $X$ be a subset of $\mathbb R^2$ and $B$ be a disc of the same area as $X$. Set $X_\epsilon$ to be the $\epsilon$-neigborhood of $X$. Then $$area\\,X_\epsilon\ge area\\,B_\epsilon.$$