$f$,$g$ : $\Omega$ $\rightarrow$ [-$\infty$,$\infty$] measurable functions.
Show that the following functions are measurable: 1) $f$ $\cdot$ $g$ 2) max{f,g} 3) $f^+$ 4) $f^-$ 5) |$f$| 6) $\alpha$ $\cdot$ $f$ + $\beta$ $\cdot$ $g$ for $\alpha$,$\beta$ $\in$ [-$\infty$, $\infty$ ] I was able to show that the functions are measurable, but only for $\mathbb{R}$, not for the extented real numbers.
We don't know that: $f$ + $g$, $\alpha$ $\cdot$ $f$are measurable. We know that: continuous functions, composition are measurable. But I don't know if this helps for my problem.
Thank you for your reply.