Absolute continuity of probability measures and conditional expectations

Abstract

In this chapter a special attention is devoted to the absolute continuity  of measures. It is shown how this notion and the Radon-Nikodym theorem work to define conditional expectations. The list of properties of conditional expectations are given here. In particular, it is emphasized the optimality in the mean-square sense of conditional expectations (see [7], [15], [19], [40], [41] and [45]).