Is it a change of variable?

Question

Hi everyone: In a book I am reading, they make a sort of "substitution" like this: let $B(0,R)$ be a ball in $\mathbb{R}^{N}$ $(N\geq2)$ and $f$ a locally integrable function. Let $\mu$ be a finite measure on $B(0,R)$. They set $$\omega:=\int_{B(o,t)}d\mu(t)$$ and then they write $$\int_{B(0,R)}f(x)d\mu(x)=\int_{0}^{R}f(t)d\omega(t).(????)$$ Can someone explain this? Thanks for you help.