Lebesgue Integral [need clarifications]

Hi all,..

i try to solve this problem, but i don't know what is the connection between convergence in measure and the integral. can someone help me. . .

Let $\displaystyle \left\{ f_{n}\right\}$ be a sequence of function and $\displaystyle f_{n}\longrightarrow f$ in measure.

Let $\displaystyle g$ be an integrable function such that $\displaystyle \left\vert f_{n}\right\vert \leq g,\forall n$.

Show that $\displaystyle %

%TCIMACRO{\dint }%

%BeginExpansion

{\displaystyle\int}

%EndExpansion

\left\vert f_{n}-f\right\vert \longrightarrow0$

thks