PlanetMath: Mann's theorem

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Mann's theorem

(Theorem)

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

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

where $\sigma$ denotes Schnirelmann density.

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

"Mann's theorem" is owned by bbukh.

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Other names:

$(\alpha+\beta)$ -conjecture

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Cross-references: Schnirelmann density, subsets

This is version 2 of Mann's theorem, born on 2002-12-28, modified 2002-12-30.
Object id is 3857, canonical name is MannsTheorem.
Accessed 2965 times total.

Classification:

AMS MSC:	11B05 (Number theory :: Sequences and sets :: Density, gaps, topology)
	11B13 (Number theory :: Sequences and sets :: Additive bases)

Pending Errata and Addenda

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