Maximal ergodic theorem

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.

Maximal ergodic theorem

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.