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| Abstract: We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem. Let (X, B, µ) be a probability space, T: X → X a (possibly noninvertible) measurepreserving transformation, and f ∈ L 1 (X, B, µ). Let Akf = 1 k−1 � k j=0 fT j, f ∗ N = sup | |||||||||||||||
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