Maximal ergodic theorem
Let (X,ℬ,μ) be a probability space and T:X→X a measure preserving transformation. Let f be a L1(μ) function.
Define the averages
f*(x)=sup |
Then, for any , we have:
This theorem may be used in the proof of the ergodic theorem (also known as Birkhoff ergodic theorem, or pointwise or strong ergodic theorem)
Title | Maximal ergodic theorem |
---|---|
Canonical name | MaximalErgodicTheorem |
Date of creation | 2014-03-19 22:15:48 |
Last modified on | 2014-03-19 22:15:48 |
Owner | Filipe (28191) |
Last modified by | Filipe (28191) |
Numerical id | 3 |
Author | Filipe (28191) |
Entry type | Theorem |
Related topic | birkhoff ergodic theorem |