Why the theorem of Scheffé should be rather called a theorem of Riesz
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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 (fn) 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.
Key words and phrasesSheffé theorem convergence in total variation characterization of Lp-convergence
Mathematics subject classification number01A60 28A20
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