Let $F \ge 0$ be the distribution function of $\mu_F$. I could already show that $G:=F^2$ is a distribution function of a measure $\mu_G$ and that $\mu_G << \mu_F$.
Now I need to determine the density $\frac{d\mu_G}{d\mu_F}$. We have never worked with densities before and I'm knew to this notation, is it simplify the fraction of the derivatives or how is this done?