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.

Key words and phrases

Sheffé theoremconvergence in total variationcharacterization of L_{
p
}-convergence