This lecture will be a continuation of my October lecture on a program to categorify measure theory. After a quick reminder of some of the basic concepts like the finite Grothendieck topology and cosheaves, and the basic theorem on the (bi)representability of the the cosheaf category, I will try to demonstrate that all the work gone into setting up the machinery was not in vain by first, giving categorified versions of some basic theorems of measure theory (e.g. Fubini and Fubini-Tonelli) and second, by explaining some of the rich structure underlying categorified measure theory, a blend of analysis, algebraic geometry and topos theory.