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  • Author or Editor: Norbert Kusolitsch x
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In 1947 Henry Scheffé published a result which afterwards became known as Scheffé’s theorem, stating that the distributions of a sequence (f n ) of densities, which converge almost everywhere to a density f, converge uniformly to the distribution of f. But almost 20 years earlier Frigyes Riesz proved a sufficient condition for convergence in the p-th mean (p ≥ 1), wherefrom the Scheffé theorem is just a special case.

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In this note the proof of a slight generalization of the Maximal Ergodic Inequality is a bit simplified and it is shown that from this generalized inequality Birkhoff’s Pointwise Ergodic Theorem follows almost immediately.

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