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
- Keane, Michael; Petersen, Karl (2006), "Easy and nearly simultaneous proofs of the Ergodic Theorem and Maximal Ergodic Theorem", Institute of Mathematical Statistics Lecture Notes - Monograph Series, Institute of Mathematical Statistics Lecture Notes - Monograph Series, 48: 248–251, ISBN 0-940600-64-1, doi:10.1214/074921706000000266.
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