Mann's theorem

Statement

Suppose $A$ and $B$ are subsets of ${\mathbb{N}}_0$, both containing $0$. Define $A+B$ to be the set of all integers of the form $a+b$, with $a\in A,b\in B$. if $\sigma$ denotes the Schnirelmann density, then:

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

Equality need not hold.

Related facts

Weaker facts

• Schnirelmann's theorem on Goldbach's conjecture