2.1 Overview

We’ll look at three types of conditional distributions, depending on the type of objects we condition on: sets, \(\sigma\)-algebras (or random variables), and sets of measure \(0\). Different applications require different levels of conditioning; in extreme cases, one may have to condition on impossible events for the sake of theoretical analysis. Typically, most courses on probability theory cover only the first level of conditioning (i.e conditioning on sets of positive measure).