, Volume 61, Issue 1-2, pp 225-229
Date: 01 Oct 2010

Why the theorem of Scheffé should be rather called a theorem of Riesz

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

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.

Dedicated to Endre Csáki and Pál Révész on the occasion of their 75th birthdays