# Mann’s theorem

Let $A$ and $B$ be subsets of $\mathbb{Z}$. If $0\in A\cap B$,

$$\sigma (A+B)\ge \mathrm{min}(1,\sigma A+\sigma B),$$ |

where $\sigma $ denotes Schnirelmann density^{}.

This statement was known also as $(\alpha +\beta )$-conjecture until H. B. Mann proved it in 1942.

Title | Mann’s theorem |
---|---|

Canonical name | MannsTheorem |

Date of creation | 2013-03-22 13:20:32 |

Last modified on | 2013-03-22 13:20:32 |

Owner | bbukh (348) |

Last modified by | bbukh (348) |

Numerical id | 5 |

Author | bbukh (348) |

Entry type | Theorem |

Classification | msc 11B05 |

Classification | msc 11B13 |

Synonym | $(\alpha +\beta )$-conjecture |

Related topic | SchnirlemannDensity |