Solution
= Solution
The sequence $(f_n)$ is <equicontinuous family of functions>[equicontinuous] on $[0,1]$ when, for every $\varepsilon>0$, there is a $\delta>0$ such that
$$
|s-t|<\delta
\Longrightarrow
|f_n(s)-f_n(t)|<\varepsilon
$$
for every $n$. The <Arzelà-Ascoli theorem> says that a uniformly bounded equicontinuous sequence of continuous real-valued functions on a compact interval has a uniformly convergent subsequence.