When I read Introduction to Dynamical Systems by Brin and Stuck, I didn't understand one detail. This is in the proof showing that expanding endomorphism is mixing. I do not understand why when $n>i$, the intersection now just has $m^{n-i}$ intervals. I get through other details in the proof, except this point.
For the definition of (strong) mixing, it is:
"A mpt $T$ on $(X,\mathcal{B},\mu)$ is called to be (strong) mixing if $$\lim_{n \to \infty} \mu(A \cap T^{-n}(B)) = \mu(A)\mu(B) ."$$
I really appreciate any help.
