In this chapter, we will introduce the basic ideas of Borel sets, measure spaces, measures and measurable functions.

Conventions

In the following section we use the convention that ${\displaystyle \,X}$ is a set and ${\displaystyle {\mathcal {P}}(X)}$ is its power set.

Usually if ${\displaystyle {\mathcal {C}}}$ is a subset of ${\displaystyle {\mathcal {P}}(X)}$ it'll be referred as class.

Sections

• 1.1 Semialgebras, Algebras and σ-algebras
• 1.2 Measures
• 1.3 Measurable Functions