[[Measure theory MOC]]
# Borel set

Given a [[topological space]] $(X, \mathcal{T})$, the set $B$ of **borel sets** is the closure of $\mathcal{T}$ as a [[σ-algebra]]. #m/def/measure 
This σ-algebra, called the **Borel algebra** on $X$, is the smallest σ-algebra containing all open sets or all closed sets.
A [[Measure space|measure]] on the [[Measure space|measurable space]] $(X,B)$ is called a **Borel measure**.


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#state/tidy | #lang/en | #SemBr