# The basic ergodic theorems, yet again

• Jairo Bochi Facultad de Matem´aticas, Pontificia Universidad Cat´olica de Chile, Chile.
Keywords: Maximal ergodic theorem, Birkhoff’s ergodic theorem, Rokhlin lemma, Kingman’s subadditive ergodic theorem

### Abstract

A generalization of Rokhlin’s Tower Lemma is presented. The Maximal Ergodic Theorem is then obtained as a corollary. We also use the generalized Rokhlin lemma, this time combined with a subadditive version of Kac’s formula, to deduce a subadditive version of the Maximal Ergodic Theorem due to Silva and Thieullen.

In both the additive and subadditive cases, these maximal theorems immediately imply that “heavy” points have positive probability. We use heaviness to prove the pointwise ergodic theorems of Birkhoff and Kingman.

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Published
2019-03-15
How to Cite
Bochi, J. (2019). The basic ergodic theorems, yet again. CUBO, A Mathematical Journal, 20(3), 81–95. https://doi.org/10.4067/S0719-06462018000300081
Section
Articles