In mathematics, a function f is superadditive if for all x and y in the domain of f. Similarly, a sequence is called superadditive if it satisfies the inequality for all m and n. The term "superadditive" is also applied to functions from a boolean algebra to the real numbers where such as lower probabilities.

Examples of superadditive functions

Properties

If f is a superadditive function whose domain contains 0, then To see this, take the inequality at the top: Hence The negative of a superadditive function is subadditive.

Fekete's lemma

The major reason for the use of superadditive sequences is the following lemma due to Michael Fekete. The analogue of Fekete's lemma holds for subadditive functions as well. There are extensions of Fekete's lemma that do not require the definition of superadditivity above to hold for all m and n. There are also results that allow one to deduce the rate of convergence to the limit whose existence is stated in Fekete's lemma if some kind of both superadditivity and subadditivity is present. A good exposition of this topic may be found in Steele (1997).