Periodica Mathematica Hungarica

, Volume 61, Issue 1, pp 225–229

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

Article

DOI: 10.1007/s10998-010-3225-6

Cite this article as:
Kusolitsch, N. Period Math Hung (2010) 61: 225. doi:10.1007/s10998-010-3225-6

Abstract

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 phrases

Sheffé theoremconvergence in total variationcharacterization of Lp-convergence

Mathematics subject classification number

01A6028A20

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2010

Authors and Affiliations

  1. 1.Institute of Statistics and Probability TheoryTechnical University WienWienAustria