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.
Thomas M. Liggett. "An Improved Subadditive Ergodic Theorem." Ann. Probab. 13 (4) 1279 - 1285, November, 1985. https://doi.org/10.1214/aop/1176992811