Maximal ergodic theorem

Let (X,,μ) be a probability spaceMathworldPlanetmath and T:XX a measure preserving transformation. Let f be a L1(μ) function. Define the averages


Then, for any λ𝐑, 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