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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
DOI: https://doi.org/10.1090/S0002-9939-1973-0315324-X
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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Article copyright: © Copyright 1973 American Mathematical Society