Korovkin sets and mean ergodic theorems.
Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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Janusz Woś (1987)
Colloquium Mathematicae
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R. Sato (1990)
Colloquium Mathematicae
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Burgess Davis (1982)
Studia Mathematica
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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...
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.
J. Woś (1987)
Colloquium Mathematicae
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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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Lasha Ephremidze (2002)
Fundamenta Mathematicae
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It is proved that the ergodic maximal operator is one-to-one.
Paweł J. Mitkowski, Wojciech Mitkowski (2012)
International Journal of Applied Mathematics and Computer Science
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We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor...
Ryotaro Sato (1995)
Studia Mathematica
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Let (X,ℱ,µ) be a finite measure space and τ a null preserving transformation on (X,ℱ,µ). Functions in Lorentz spaces L(p,q) associated with the measure μ are considered for pointwise ergodic theorems. Necessary and sufficient conditions are given in order that for any f in L(p,q) the ergodic average converges almost everywhere to a function f* in , where (pq) and are assumed to be in the set . Results due to C. Ryll-Nardzewski, S. Gładysz, and I. Assani and J. Woś are generalized...
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.
Paweł Głowacki (1981)
Studia Mathematica
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