Let $f_n:[0,1]\rightarrow \mathbb{R}$ be a continuous function for each positive integer $n$. If
$$\displaystyle\lim_{n\rightarrow \infty} \displaystyle \int_0^1 f_n(x)^2 dx=0,$$
then
$$\displaystyle\lim_{n\rightarrow \infty} f_n\left(\frac{1}{2}\right)=0.$$