In this chapter, we will introduce the basic ideas of Borel sets, measure spaces, measures and measurable functions.
In the following section we use the convention that X {\displaystyle \,X} is a set and P ( X ) {\displaystyle {\mathcal {P}}(X)} is its power set.
Usually if C {\displaystyle {\mathcal {C}}} is a subset of P ( X ) {\displaystyle {\mathcal {P}}(X)} it'll be referred as class.