An atomic theory of ergodic spaces
R. Caballero, A. de la Torre (1985)
Studia Mathematica
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Displaying similar documents to “A generalization of the individual ergodic theorem”
An atomic theory of ergodic spaces
Remarks on the tightness of cocycles
Jon Aaronson, Benjamin Weiss (2000)
Colloquium Mathematicae
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We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.
On a ratio ergodic theorem
Ryotaro Sato (1987)
Studia Mathematica
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Weights for ergodic square functions
F. J. Martin-Reyes (1986)
Annales de l'I.H.P. Probabilités et statistiques
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Ergodic power functions for mean bounded, invertible, positive operators
F. Martín-Reyes, P. Ortega Salvador (1988)
Studia Mathematica
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On the ergodic power function for invertible positive operators
Ryotaro Sato (1988)
Studia Mathematica
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A general ratio ergodic theorem for Abel sums
Ryotaro Sato (1973)
Studia Mathematica
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Weighted weak type inequalities for the ergodic maximal function and the pointwise ergodic theorem
A. de la Torre, F. Martín-Reyes (1987)
Studia Mathematica
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On the mean ergodic theorem for Cesàro bounded operators
Yves Derriennic (2000)
Colloquium Mathematicae
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For a Cesàro bounded operator in a Hilbert space or a reflexive Banach space the mean ergodic theorem does not hold in general. We give an additional geometrical assumption which is sufficient to imply the validity of that theorem. Our result yields the mean ergodic theorem for positive Cesàro bounded operators in (1 < p < ∞). We do not use the tauberian theorem of Hardy and Littlewood, which was the main tool of previous authors. Some new examples, interesting for summability...