Measure Theory/Basic Structures And Definitions

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 ${\displaystyle \,X}$ 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.

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