Some results in the theory of Riemann sums
type: Item
instance of: scholarly article
title: Some results in the theory of Riemann sums
zbMATH Open document ID: 0885.60028
author: Jean-Jacques Ruch
author: Michel Weber
published in: Expositiones Mathematicae
publication date: 1997-09-28T00:00:00Z
review text: The aim of this paper is to prove negative type results concerning the almost everywhere convergence of Riemann sums along the sequence of primes. An earlier result of \textit{W. Rudin} [Proc. Am. Math. Soc. 15, 321-324 (1964; Zbl 0132.03601)] is improved. \textit{J. Bourgain}'s entropy criterion is used [Isr. J. Math. 63, No. 1, 79-97 (1988; Zbl 0677.60042)]. See also \textit{D. Schneider} and the second author [in: Séminaire de probabilités XXVII. Lect. Notes Math. 1557, 202-206 (1993; Zbl 0799.60035)], concerning the technique of proof.
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 28D99
Mathematics Subject Classification ID: 40H05
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1051312
zbMATH Keywords: summability methods
zbMATH Keywords: Riemann sums
zbMATH Keywords: almost everywhere convergence
zbMATH Keywords: Bourgain's entropy criterion
reviewed by: Ludwig Paditz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1051312