How to comprehend the statements below?
Let $X=[0,1],f_2(x)=2x(mod1)$.$\mu$ is a measure such that $f_2$ is ergodic.The positive entropy assumption $h_\mu(f_2)>0$ implies that the restriction of $f_2$ to the support of $\mu$ is not invertible. Equivalently, we can always find some pairs of $\mu$ generic points with the same image under $f_2$.
If $f_2$ is invertable on $supp\ \mu$ then one of the preimage of small interval inherit the measure of the interval and the other is zero measure set. Then use Shannon's theorem about measure entropy to show that $h_2(f)=0$,a contradiction.