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A Quantitative Version of a de Bruijn-Post Theorem

✍ Scribed by Simonetta Salvati; Aljoša Volčič

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 176 KB
Volume: 229
Category: Article
ISSN: 0025-584X
DOI: 10.1002/1522-2616(200109)229:1<161::aid-mana161>3.0.co;2-0

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✦ Synopsis

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 n i=1 f (x i ) do not admit a limit. In this paper we will prove a quantitative version of this result and we will extend it to functions with values in IR d .

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