Un théorème ergodique presque sous-additif. (An almost subadditive ergodic theorem). (French) Zbl 0586.28014

Derriennic, Yves

Ann. Probab. 11, 669-677 (1983).

The author establishes \((L^ 1\) and ”almost everywhere”) convergence results for ”almost subadditive processes”. These are suitable perturbations of the subadditive processes introduced by Kingman. These theorems extend Kingman’s results and give as a corollary the Shannon- McMillan-Breiman information theorem.

Reviewer: N.Ghoussoub

MSC:

28D05	Measure-preserving transformations
60G10	Stationary stochastic processes
60F15	Strong limit theorems
28D20	Entropy and other invariants

Keywords:

extension of Kingman’s subadditive ergodic theorem; almost subadditive sequence; entropy; measure-preserving transformations; subadditive processes; Shannon-McMillan-Breiman information theorem