Signed measures, complex measures, and absolute continuity

Abstract

Given a measure, a signed measure, or a complex measure μ on a measurable space (X, S), there are frequently other measures nearby that are closely related to μ in one way or another. These measures can often be put to good use in explicating various properties of μ. In the same vein, given two measures μ and ν (on the same or different measurable spaces), there are often useful ways in which they can be related and other ways of constructing new measures from the pair. In this chapter we explore some of the most important of these constructions and relations.