A Quantitative Version of a de Bruijn-Post Theorem |
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| Authors: | Simonetta Salvati Aljoša Volčič |
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| Institution: | Dipartimento di Matematica, Università degli Studi di Trieste, Piazzale Europa, 1, 34127 Trieste, Italy |
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| 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 { xi} such that the averages  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 ℝd. |
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| Keywords: | Riemann integral uniformly distributed sequence |
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