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Suppose A {\displaystyle A} and B {\displaystyle B} are subsets of N 0 {\displaystyle \mathbb {N} _{0}} , both containing 0 {\displaystyle 0} . Define A + B {\displaystyle A+B} to be the set of all integers of the form a + b {\displaystyle a+b} , with a ∈ A , b ∈ B {\displaystyle a\in A,b\in B} . if σ {\displaystyle \sigma } denotes the Schnirelmann density, then:
σ ( A + B ) ≥ min { 1 , σ ( A ) + σ ( B ) } {\displaystyle \sigma (A+B)\geq \min\{1,\sigma (A)+\sigma (B)\}} .
Equality need not hold.
