A measure $\mu$ dominates another measure $\nu$ whenever $\mu=0$ implies $\nu=0$. If I would like to take the integral of a measurable function $f_0$, say the density function of the probability measure $F_0$ over the real numbers w.r.t. a dominating measure say $\mu=F_0+F_1$ ($F_1$ being another probability measure), I will have $$\int f_0 \mbox{d}\mu=1$$ If $\mu$ is Lebesgue measure the result is obvious to me. Whenever $\mu=F_0+F_1$, I dont understand why $$\int f_0 \mbox{d}(F_0+F_1)=\int f_0 \mbox{d}F_0+\int f_0 \mbox{d} F_1=1$$ should be true. I have some missing information here. Does somebody know why it should it be the case? Here is the related paper: just the first page where this definition is made.
Thank you very much.