# Brunn-Minkowski inequality

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

 $\operatorname{vol}(A+B)^{1/d}\geq\operatorname{vol}(A)^{1/d}+\operatorname{vol% }(B)^{1/d},$

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

## References

• 1 Jiří Matoušek. Lectures on Discrete Geometry, volume 212 of GTM. Springer, 2002. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0999.52006Zbl 0999.52006.
Title Brunn-Minkowski inequality BrunnMinkowskiInequality 2013-03-22 13:58:20 2013-03-22 13:58:20 bbukh (348) bbukh (348) 7 bbukh (348) Theorem msc 51M16