Additive and superadditive local theorems

Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T= $T_{t}$ : t < 0 be a strongly continuous semigroup of positive linear operators on the Banach lattice L. Under some suitable norm conditions on L we prove a general differentiation theorem for superadditive processes in L with respect to the semigroup T.

Kingman's subadditive ergodic theorem

J. Michael Steele (1989)

Annales de l'I.H.P. Probabilités et statistiques

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The quasi-sure ratio ergodic theorem

P. J. Fitzsimmons (1998)

Annales de l'I.H.P. Probabilités et statistiques

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