# Measure Theory/Basic Structures And Definitions

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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 $\,X$ is a set and ${\mathcal {P}}(X)$ is its power set.

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