Loading AI tools
Property of a function From Wikipedia, the free encyclopedia
In mathematics, a function is superadditive if for all and in the domain of
Similarly, a sequence is called superadditive if it satisfies the inequality for all and
The term "superadditive" is also applied to functions from a boolean algebra to the real numbers where such as lower probabilities.
If is a superadditive function whose domain contains then To see this, take the inequality at the top: Hence
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 and 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]
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.