Let $g$:$RR$ be a measurable function such that ${\displaystyle \underset{X}{\overset{\phantom{}}{}}}|g|dm<mi\; id="EditorElement\_518917"></mi><mtext\; id="EditorElement\_518889"></mtext><mi\; id="EditorElement\_518890">(</mi>$here $m$ is the Lebesgue measure$).$ Show that $\underset{n}{lim}({\displaystyle \underset{n}{\overset{n}{}}}|g(x)|dx+{\displaystyle \underset{-}{\overset{-n}{}}}|g(x)|dx)=0.$