If $f_n \rightarrow f$ in measure and $|f_n|\leq g$ where $g$ is a integrable function, then $\int |f_n-f|$ is integrable?
If $f_n \rightarrow f$ in measure and $|f_n|\leq g$ where $g$ is a integrable function, then $\int |f_n-f|$ is integrable?