summable square function implies...? I have difficulty to demonstrate this:
$$ \int_{-\infty}^{\infty}|f(x)|^2dx<\infty~~~\text{(summable square function)}$$ 
then, 
$$\lim_{|x|\rightarrow\infty }f(x)=0$$
thank you.

You are probably having difficulties because this fact is false: The function $$f(x)=\begin{cases} 1 & x \in \mathbb Z \\0 & x \notin \mathbb Z \end{cases}$$ is a counterexample.
