Borel set

Given a topological space $(𝑋, T)$ , the set $𝐵$ of borel sets is the closure of $T$ as a σ-algebra. 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 on the measurable space $(𝑋, 𝐵)$ is called a Borel measure.