Fekete’s subadditive lemma

Let (an)n be a subadditive sequence in [-,). Then, the following limit exists in [-,) and equals the infimumMathworldPlanetmath of the same sequence:


Although the lemma is usually stated for subadditive sequences, an analogue conclusionMathworldPlanetmath is valid for superadditive sequences. In that case, for (an)n a subadditive sequence in (-,], one has:


The proof of the superadditive case is obtained by taking the symmetric sequence (-an)n and applying the subadditive version of the theorem.

Title Fekete’s subadditive lemma
Canonical name FeketesSubadditiveLemma
Date of creation 2014-03-19 22:15:10
Last modified on 2014-03-19 22:15:10
Owner Filipe (28191)
Last modified by Filipe (28191)
Numerical id 4
Author Filipe (28191)
Entry type Theorem