The Pointwise Ergodic Theorem

  • Yves Coudène
Part of the Universitext book series (UTX)


Consider a dynamical system, modeled by the data of a phase space X, a transformation T: X → X describing the evolution of the system over time, and a finite measure μ representing an extensive quantity conserved during the motion. We wish to study the sequence {T n (x)}n ∈ N, which represents the succession of states the system takes on over time. This sequence makes up the trajectory of the point x, or its orbit.


Conditional Expectation Ergodic Theorem Finite Measure Observable Quantity Maximal Inequality 
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  1. 13.
    Krengel, U.: Ergodic Theorems. de Gruyter Studies in Mathematics, vol. 6. Walter de Gruyter & Co., Berlin (1985)Google Scholar

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© Springer-Verlag London 2016

Authors and Affiliations

  • Yves Coudène
    • 1
  1. 1.Université de Bretagne OccidentaleBrestFrance

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