The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics. Suppose that ( X , B , μ ) {\displaystyle (X,{\mathcal {B}},\mu )} is a probability space, that T : X → X {\displaystyle T:X\to X} is a (possibly noninvertible) measure-preserving transformation, and that f ∈ L 1 ( μ , R ) {\displaystyle f\in L^{1}(\mu ,\mathbb {R} )} .
The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics. Suppose that ( X , B , μ ) {\displaystyle (X,{\mathcal {B}},\mu )} is a probability space, that T : X → X {\displaystyle T:X\to X} is a (possibly noninvertible) measure-preserving transformation, and that f ∈ L 1 ( μ , R ) {\displaystyle f\in L^{1}(\mu ,\mathbb {R} )} .
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