An Improved Subadditive Ergodic Theorem

Abstract

A new version of Kingman's subadditive ergodic theorem is presented, in which the subadditivity and stationarity assumptions are relaxed without weakening the conclusions. This result applies to a number of situations that were not covered by Kingman's original theorem. The proof involves a rather simple reduction to the additive case, where Birkhoff's ergodic theorem can be applied.