This chapter introduces signed measures and provides with the Hahn-Jordan decomposition a method to represent a signed measure uniquely as a difference of finite measures. We say that a signed measure is absolutely continuous with respect to a \(\sigma \) -finite measure if whenever the \(\sigma \) -finite measure assigns zero to a set, the signed measure does this as well. The theorem of Radon-Nikodym provides in this case a unique representation for the signed measure as a Lebesgue integral where the integrator is the \(\sigma \) -finite measure, and the integrand will be called the Radon-Nikodym derivative. The proof uses the Hahn-Jordan decomposition. The chapter then continues with the existence and the definition of conditional expectation, its properties, and its connection to conditional probability. The chapter ends with a closed form formula for the conditional expectation in the case in which the integrand consists of a measurable function of two random variables where one is measurable and the other one is independent of the \(\sigma \) -algebra used for conditioning.