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I'd like some help with this question: Show that the sequence $f_n$ defined by $f_n=n\chi_{[\frac{1}{n},\frac{2}{n}]}$ have the following property: given $\delta > 0$, it converges uniformly in $[ 0,\delta ]^C$ Thanks.

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    As soon as $n\gt2/\delta$, $f_n$ is identically zero in the complement of $[0,\delta]$. Does that help?2011-06-03
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    Yes, thanks for the answer.2011-06-03

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Look at what happens when you have $n > \frac{2}{\delta}$. In particular what is $f_n$ on $[0,\delta]^c$ when $n > \frac{2}{\delta}$.