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# Mann’s theorem

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

$\sigma(A+B)\geq\min(1,\sigma A+\sigma B),$ |

where $\sigma$ denotes Schnirelmann density.

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

Related:

SchnirlemannDensity

Synonym:

$(\alpha+\beta)$-conjecture

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

11B05*no label found*11B13

*no label found*

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