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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A very slowly convergent sequence of continuous functions


Author: Walter Rudin
Journal: Proc. Amer. Math. Soc. 39 (1973), 647-648
MSC: Primary 40A05
MathSciNet review: 0315324
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Abstract: A sequence of continuous functions $ {f_n}:[0,1] \to (0,1]$ is constructed, with $ {\lim _{n \to \infty }}{f_n}(x) = 0$ for every $ x \in [0,1]$, but such that to every unbounded sequence $ \{ {\lambda _n}\} $ of positive numbers corresponds a point $ x \in [0,1]$ at which $ \lim {\sup _{n \to \infty }}{\lambda _n}{f_n}(x) = \infty $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0315324-X
PII: S 0002-9939(1973)0315324-X
Article copyright: © Copyright 1973 American Mathematical Society