In mathematics, a function is superadditive in the domain

Similarly, a sequence is called superadditive if it satisfies the inequality

The term "superadditive" is also applied to functions from a boolean algebra such as lower probabilities.

Examples of superadditive functions

• is a superadditive function for nonnegative real numbers

  The determinant is superadditive for nonnegative Hermitian matrix This follows from the Minkowski determinant theorem is superadditive (equivalently, concave)

• Horst Alzer proved that Hadamard's gamma function

• Mutual information

Properties

in the defining inequality.

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.

1. Lemma: the limit is equal to the supremum for example.)

The analogue of Fekete's lemma holds for subadditive 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).

See also

References

Notes