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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

  • 0
    Hint: Which structure has the collection of the Borel subsets $A$ of $\mathbb R$ such that the integral of $f$ on $A$ is zero?2012-06-13
  • 0
    I think the borel set $F_{\delta}$2012-06-14
  • 0
    is $\mathrm{d}m$ Lebesgue measure?2012-07-08

3 Answers 3