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Complementability and Maximality in Different Contexts: Ergodic Theory, Brownian and Poly-Adic Filtrations

  • Christophe LeuridanEmail author
Chapter
First Online:
Part of the Lecture Notes in Mathematics book series (LNM, volume 2252)

Abstract

The notions of complementability and maximality were introduced in 1974 by Ornstein and Weiss in the context of the automorphisms of a probability space, in 2008 by Brossard and Leuridan in the context of the Brownian filtrations, and in 2017 by Leuridan in the context of the poly-adic filtrations indexed by the non-positive integers. We present here some striking analogies and also some differences existing between these three contexts.

Keywords

Automorphisms of Lebesgue spaces Factors Entropy Filtrations indexed by the non-positive integers Poly-adic filtrations Brownian filtrations Immersed filtrations Complementability Maximality Exchange property 
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Notes

Acknowledgements

I thank A. Coquio, J. Brossard, M. Émery, S. Laurent, J.P. Thouvenot for their useful remarks and for stimulating conversations.

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Authors and Affiliations

  1. 1.Institut FourierUniversité Grenoble AlpesGrenobleFrance

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