Periodica Mathematica Hungarica

, Volume 61, Issue 1–2, pp 225–229

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


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


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 theorem convergence in total variation characterization of Lp-convergence 

Mathematics subject classification number

01A60 28A20 

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2010

Authors and Affiliations

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

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