We have seen that if f is a non-negative measurable function, then its indefinite integral _ (with respect to μ) is a measure. We may visualize the relation between μ, f, and _ as, d_ = fdμ. That is, the “derivative of _ with respect to μ equals f”. We now make this and related ideas precise, by introducing the concept of absolute continuity of measures and prove a crucial result namely, the Radon-Nikodym theorem. The concept of conditional probability and expectation in Chapter 23 is based on this theorem.