Superadditivity

In mathematics, a function

in the domain of

Similarly, a sequence

is called superadditive if it satisfies the inequality

The term "superadditive" is also applied to functions from a boolean algebra to the real numbers where

such as lower probabilities.

is a superadditive function whose domain contains

To see this, take the inequality at the top:

The negative of a superadditive function is subadditive.

The major reason for the use of superadditive sequences is the following lemma due to Michael Fekete.

[3] 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

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).

[4][5] Notes This article incorporates material from Superadditivity on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.