Maximal ergodic theorem
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The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics.
Suppose that is a probability space, that is a (possibly noninvertible) measure-preserving transformation, and that . Define by
Then the maximal ergodic theorem states that
for any λ ∈ R.
This theorem is used to prove the point-wise ergodic theorem.
References
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