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 $S$.

Title	Brunn-Minkowski inequality
Canonical name	BrunnMinkowskiInequality
Date of creation	2013-03-22 13:58:20
Last modified on	2013-03-22 13:58:20
Owner	bbukh (348)
Last modified by	bbukh (348)
Numerical id	7
Author	bbukh (348)
Entry type	Theorem
Classification	msc 51M16