Suppose I have a function $|1_A f|$, is it possible to take the $1_A$ out of the absolute value in an integral. I.e. is this correct? $$\int_\Omega |1_A f| d\mu=\int_\Omega 1_A |f|d\mu=\int_A|f| d\mu\leq \int_\Omega |f| d\mu$$
This seems obviously true as $1_A$ is just 0 or 1 but im not positive.