# Brunn-Minkowski inequality

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

## 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^{} |
---|---|

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 |