The basic ergodic theorems, yet again
Author
Bochi, Jairo
Full text
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/206910.4067/S0719-06462018000300081
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.