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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.
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The maximalergodictheorem is a theorem in ergodic theory, a discipline within mathematics. Suppose that ( X , B , μ ) {\displaystyle (X,{\mathcal {B}}...
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2008. Retrieved 7 October 2014. Bourgain, Jean (1988). "On the maximalergodictheorem for certain subsets of the integers". Israel Journal of Mathematics...
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Foreman, Matthew; Weiss, Benjamin (2004). "An anti-classification theorem for ergodic measure-preserving transformations". Journal of the European Mathematical...