be $G\subseteq \mathbb{R}$ a open set. Be $f:G\rightarrow \mathbb{R}$* measured and for all interval $[a,b] \subseteq G$ to have that $f$ is lebesgue integrable function in $[a,b]$ and $\int_{a}^b f dm=0$. Show that $f=0$ almost everywhere.
I know that if for all set measured $A\subseteq E$, if $\int_{A}f=0$ so $f=0$ almost everywhere, I try to use this for the problem but dont work.
thanks