Superadditivity

In mathematics, a function ${\displaystyle f}$ is superadditive if ${\displaystyle f(x+y)\geq f(x)+f(y)}$ for all ${\displaystyle x}$ and ${\displaystyle y}$ in the domain of ${\displaystyle f.}$

Similarly, a sequence ${\displaystyle a_{1},a_{2},\ldots }$ is called superadditive if it satisfies the inequality $${\displaystyle a_{n+m}\geq a_{n}+a_{m}}$$ for all ${\displaystyle m}$ and ${\displaystyle n.}$

The term "superadditive" is also applied to functions from a boolean algebra to the real numbers where ${\displaystyle P(X\lor Y)\geq P(X)+P(Y),}$ such as lower probabilities.