Brunn-Minkowski inequality

Let $A$ and $B$ be non-empty compact subsets of ${ℝ}^d$.Then

$$\mathrm{vol}{(A+B)}^{1/d}\ge \mathrm{vol}{(A)}^{1/d}+\mathrm{vol}{(B)}^{1/d},$$

where $A+B$ denotes the Minkowski sum of $A$ and $B$, and $\mathrm{vol}(S)$ denotes the volume of $S$.