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The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics.
Suppose that (X, \mathcal{B}, \mu) is a probability space, that T : X \to X is a (possibly noninvertible) measure-preserving transformation, and that f \in L^1(\mu). Define f^* by
Then the maximal ergodic theorem states that
for any λ ∈ R.
This theorem is used to prove the point-wise ergodic theorem.
Logic, Set theory, Statistics, Number theory, Mathematical logic
Mathematics, Number theory, Geometry, Probability theory, Chaos theory