Let $(S,\mathcal{A})$ be a measurable space. Let $f:S\to\mathbb{R}$ be a measurable function and let $p\in(0,\infty)$.
Exercise: Show that $|f|^p$ is a measurable function.
Question: What does $|f|^p$ mean in this context? Is it just the absolute value of $f$ to the power $p$? E.g. $f(x) = -3x$ and $|f|^p$ gives $f(x) = \left|-3x\right|^p$? I'm confused because the notation in my textbook isn't quite consistent and this way of writing has also been used to indicate norms of series.
Thanks in advance!