Abstract
A functional ergodic theorem is proved for subadditive families of measurable functions $$(h_{k,n}\mid (k,n)\in D)$$ , where $$D\subset {\mathbb {N}}^2$$ is an additive semigroup and subadditivity means that $$h_{k_1+k_2,n_1+n_2}\le h_{k_1,n_1}+h_{k_2,n_2}\circ f^{n_1}$$ for some measure-preserving transformation f.
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