# Measure Theory/Basic Structures And Definitions

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.