A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. III. Relative isomorphism of non-ergodic transformations
Štefan Šujan (1985)
Kybernetika
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Displaying similar documents to “Some thoughts about Segal's ergodic theorem”
A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. III. Relative isomorphism of non-ergodic transformations
Ergodic seminorms for commuting transformations and applications
Bernard Host (2009)
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Recently, T. Tao gave a finitary proof of a convergence theorem for multiple averages with several commuting transformations, and soon thereafter T. Austin gave an ergodic proof of the same result. Although we give here another proof of the same theorem, this is not the main goal of this paper. Our main concern is to provide tools for the case of several commuting transformations, similar to the tools successfully used in the case of a single transformation, with the idea that they may...
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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.
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Nishishiraho, Toshihiko (1998)
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Convergence of multiple ergodic averages along cubes for several commuting transformations
Qing Chu (2010)
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We prove the norm convergence of multiple ergodic averages along cubes for several commuting transformations, and derive corresponding combinatorial results. The method we use relies primarily on the "magic extension" established recently by B. Host.
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Janusz Woś (1987)
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Roger Jones (1980)
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Karl Petersen, Shizuo Kakutani (1981)
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Yves Derriennic (2010)
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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...
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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.