A quantitative version of a de Bruijn-Post theorem

Authors
Salvati, S Volcic, AA
Citation
S. Salvati et Aa. Volcic, A quantitative version of a de Bruijn-Post theorem, MATH NACHR, 229, 2001, pp. 161-173
Citations number
8
Categorie Soggetti
Mathematics
Journal title
MATHEMATISCHE NACHRICHTEN
ISSN journal
0025584X → ACNP
Volume
229
Year of publication
2001
Pages
161 - 173
Database
ISI
SICI code
0025-584X(2001)229:<161:AQVOAD>2.0.ZU;2-B
Abstract
A theorem due to DE BRUIJN and POST states that if a real valued function f defined on [0, 1] is not Riemann-integrable, then there exists a uniformly distributed sequence {x(i)} such that the averages 1/n Sigma (n)(i=1) f(x( i)) do not admit a limit. In this paper we will prove a quantitative versio n of this result and we will extend it to functions with values in R-d.