The basic ergodic theorems, yet again
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...
Guardado en:
| Autor principal: | |
|---|---|
| Lenguaje: | English |
| Publicado: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2018
|
| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462018000300081 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | 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. |
|---|