Converges Uniformly Example

Question

Folland's Real Analysis/Measure Theory textbook on page 61 states that, $n \chi_{[0,1/n]}$ converges uniformly to 0.

I cannot see how this can be true as I thought that $\sup|f_n(x)-f(x)|$=$\sup |n \chi_{[0,1/n]}-0|=n$ which goes to $ \infty$ as $n$ approaches $\infty$, so it cannot converge uniformly to $0$. Am I mistaken or is there a typo in the textbook? I looked at the errata but I don't see anything listed. Thanks.

Answer 1

On pg 61 of Folland, of which this is example (iii)

It is worded like

In (i), (ii), (iii), $f_n \rightarrow 0$ uniformly, pointwise, and a.e. respectively.

So for this third example, it is just meant a.e convergence. Uniform convergence applies to the (i) example, which is $n^{-1}\chi_{(0,n)} $.