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Cubo (Temuco)

On-line version ISSN 0719-0646


BOCHI, Jairo. The basic ergodic theorems, yet again. Cubo [online]. 2018, vol.20, n.3, pp.81-95. ISSN 0719-0646.

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.

Keywords : Maximal ergodic theorem; Birkhoff’s ergodic theorem; Rokhlin lemma; Kingman’s subadditive ergodic theorem..

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