Let $\displaystyle f_n \rightarrow f$ in $\displaystyle L^2(X,F,m)$.
If $\displaystyle m(X)<\infty$, then $\displaystyle \int_X f_n \rightarrow \int_X f$.
any hint would be appreciated.
Let $\displaystyle f_n \rightarrow f$ in $\displaystyle L^2(X,F,m)$.
If $\displaystyle m(X)<\infty$, then $\displaystyle \int_X f_n \rightarrow \int_X f$.
any hint would be appreciated.