Mann's theorem MannsTheorem 2002-12-28 18:42:50 2002-12-30 00:47:23 Theorem \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} 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.