TITLE: If $f$ and $g$ are integrable then is $\max\{f,g\}$?
QUESTION [6 upvotes]: Possible Duplicate:
Is the pointwise maximum of two Riemann integrable functions Riemann integrable?

Let $f$ and $g$ be two integrable real functions. Is this leads that $\max\{f,g\}$ is integrable too?
Any proof?
Thanks

REPLY [12 votes]: $$
|\max(f,g)|\leqslant\max(|f|,|g|)\leqslant|f|+|g|
$$