Superadditivity

In mathematics, a sequence { a_n }, n ≥ 1, is called superadditive if it satisfies the inequality

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

Lemma: (Fekete) For every superadditive sequence { a_n }, n ≥ 1, the limit lim a_n/n exists and is equal to sup a_n/n. (The limit may be positive infinity, for instance, for the sequence a_n = log n!.)