If $f_n \rightarrow f$ in $L^p$ and $g_n \rightarrow g$ in $L^q$, where $\frac{1}{p} + \frac{1}{q} = 1$, show that $f_n g_n \rightarrow fg$ in $L^1$
Sequence of a product of functions in $L^p. L^q$ with $p,q$ conjugate