A note on a mean ergodic theorem
A. Al-Hussaini (1974)
Annales Polonici Mathematici
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Yves Derriennic (2010)
Colloquium Mathematicae
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The aim of this short note is to present in terse style the meaning and consequences of the "filling scheme" approach for a probability measure preserving transformation. A cohomological equation encapsulates the argument. We complete and simplify Woś' study (1986) of the reversibility of the ergodic limits when integrability is not assumed. We give short and unified proofs of well known results about the behaviour of ergodic averages, like Kesten's lemma (1975). The strikingly simple...
Janusz Woś (1987)
Colloquium Mathematicae
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Roland Zweimüller (2004)
Colloquium Mathematicae
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We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.
Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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Rao, M.B. (1978)
Portugaliae mathematica
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Karl Petersen, Shizuo Kakutani (1981)
Monatshefte für Mathematik
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S. Doplicher, D. Kastler (1968)
Recherche Coopérative sur Programme n°25
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Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)
Studia Mathematica
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We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
J. Woś (1987)
Colloquium Mathematicae
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Emmanuel Lesigne (1995)
Commentationes Mathematicae Universitatis Carolinae
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If is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.
R. Sato (1990)
Colloquium Mathematicae
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