So I had this question on a recent test and I wasn't able to do it.
Let $g(x)$ be integrable and let $\{f_n\}$ be a sequence of measurable functions such that $|f_n|\leq g(x)$ and $f_n\rightarrow f$ almost everywhere. I want to show that $\int |f_n-f|\rightarrow 0$.
I think the solution some how involves the Lebesgue convergence theorem, but I don't know how to apply it. I could use some help.
Thanks.