I am given $f,f' \in L^1(\mathbb{R})$, and f is absolute continuous, I want to show that:
$\lim_{|x|\rightarrow \infty} f(x)= 0$
Not sure how to show this, I know that $f(x)=\int_0^x f'(t) \, dt+f(0)$, and I can assume without loss of generality that $f(0)=0$, any help?
Thanks in advance.