Why the theorem of Scheffé should be rather called a theorem of Riesz
- First Online:
- Cite this article as:
- Kusolitsch, N. Period Math Hung (2010) 61: 225. doi:10.1007/s10998-010-3225-6
- 200 Downloads
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.