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A quantitative version of Picard's theorem

✍ Scribed by Walter Bergweiler


Book ID
112781353
Publisher
Springer Netherlands
Year
1996
Tongue
English
Weight
182 KB
Volume
34
Category
Article
ISSN
0004-2080

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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 thi