Geodesic
A ratio limit theorem for contraction projections and applications
Glasgow mathematical journal, Tome 14 (1973) no. 1, pp. 80-85

Voir la notice de l'article provenant de la source Cambridge University Press

The similarities between martingale convergence theory and pointwise ergodic theory are now well known [5, 7, 9, 10]. In [5] the similarity between the proofs of the Hopf– Dunford–Schwartz individual ergodic theorem and the martingale convergence theorem is systematically exploited to produce very general ” maximal ergodic ” inequalities for certain sequences of contractions on L1-spaces. A different approach by Rota [10] and Rao [9] leads to a unified convergence theory for martingales and Abel limits. Bishop [1] has produced ” upcrossing” inequalities which yield both theChacon-Ornstein theorem [4] and the martingale convergence theorem. 
Kopp, P. E. A ratio limit theorem for contraction projections and applications. Glasgow mathematical journal, Tome 14 (1973) no. 1, pp. 80-85. doi: 10.1017/S0017089500001774
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