Displaying similar documents to “A property of ergodic flows”

On subrelations of ergodic measured type III equivalence relations

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.

Hopf's ratio ergodic theorem by inducing

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.

Ergodic theorem, reversibility and the filling scheme

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...

Operators with an ergodic power

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.

On the sequence of integer parts of a good sequence for the ergodic theorem

Emmanuel Lesigne (1995)

Commentationes Mathematicae Universitatis Carolinae

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If ( u n ) is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts ( [ u n ] ) good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.