I am looking at the below proof. However, I can't figure out how, from the lower bound we obtain for the transition kernel below, the density for the measure $\nu_1$ is defined as below. Namely, I don't understand where the denominator comes from. Also, for the lower bound, should we not have the maximum of $a^2,b^2$ from $C = [a,b]$ instead of $a^2 \wedge b^2$? I would greatly appreciate any help.
Not sure if this is the problem here but $\wedge$ sometimes means maximum of the things. Not a particular fan of this notation. For reference see [1].
[https://en.wikipedia.org/wiki/Join_and_meet][1]