Some Open Problems in Ergodic Theory
Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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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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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Janusz Woś (1987)
Colloquium Mathematicae
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Burgess Davis (1982)
Studia Mathematica
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J. 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.
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...
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...
Charles Pugh, Michael Shub (1971)
Compositio Mathematica
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Paweł Głowacki (1981)
Studia Mathematica
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Karl Petersen, Shizuo Kakutani (1981)
Monatshefte für Mathematik
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Alexandre Danilenko (2000)
Colloquium Mathematicae
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We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
S. Doplicher, D. Kastler (1968)
Recherche Coopérative sur Programme n°25
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