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Cours Année : 2023

THE ERGODIC THEOREM

Emmanuel Lesigne

Résumé

We give here a self-contained proof of the ergodic theorem for a measure preserving action of the additive group of real numbers. There are two versions of this theorem : von Neumann ergodic theorem gives a convergence in the mean ; Birkhoff ergodic theorem gives a pointwise convergence. Nothing original here, but a direct access to a complete proof which can be useful to non specialists of the subject.
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Dates et versions

hal-04012715 , version 1 (03-03-2023)

Identifiants

  • HAL Id : hal-04012715 , version 1

Citer

Emmanuel Lesigne. THE ERGODIC THEOREM. Master. France. 2023, pp.8. ⟨hal-04012715⟩
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