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A ratio limit theorem for contraction projections and applications

Published online by Cambridge University Press:  18 May 2009

P. E. Kopp
P. E. Kopp
Affiliation:
University of Hull
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 1 , February 1973 , pp. 80 - 85
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

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