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Let $A$ and $B$ be subsets of $\mathbb{Z}$ If $0 \in A \cap B$ \begin{equation*} \sigma(A+B)\geq \min(1,\sigma A + \sigma B), \end{equation*}where $\sigma$ denotes Schnirelmann density.
This statement was known also as $(\alpha+\beta)$ conjecture until H. B. Mann proved it in 1942.
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"Mann's theorem" is owned by bbukh.
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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 3805 times total.
Classification:
| AMS MSC: | 11B05 (Number theory :: Sequences and sets :: Density, gaps, topology) | | | 11B13 (Number theory :: Sequences and sets :: Additive bases) |
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Pending Errata and Addenda
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