An ergodic theorem is proved which extends the subadditive ergodic theorem of Kingman and the Banach valued ergodic theorem of Mourier. The theorem is applied to several problems, in particular to a problem on empirical distribution functions.
"Vector Valued Subadditive Processes and Applications in Probability." Ann. Probab. 8 (1) 83 - 95, February, 1980. https://doi.org/10.1214/aop/1176994826