Supose $(f_n)$ be such that $\int|f_n-f|\to 0$, where $(f_n)$ is Lebesgue integrable. Show that $\int_E f_n \to \int_E f$ for all Lebesgue measurable sets $E$, and furthermore that $\int f_n^+\to \int f^+$.
(here $f^+$ denotes $f \vee0$)
Not sure where to start on this. Any hints to begin would be helped. thanks.