Mann’s theorem

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

$$\sigma (A+B)\ge \min (1,\sigma A+\sigma B),$$

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