I am studying functional analysis and I have stumbled upon the following inequality for $f$ continous and $\mu$ complex measure $$\lvert\int_{K}f\ d\mu\rvert\leq\int_{K}\lvert f\rvert d\lvert \mu \rvert \leq \| f \| \lvert\mu\rvert(K).$$
My question is, what does $d\lvert\mu\rvert$ denote in this context, there is a note saying that it's variation of measure, is that same as variation of function, or is there something I'm missing?