Borel algebra
The smallest 20231205121417-sigma_algebra containing (generated) by the open subsets of is called the Borel -algebra or the Borel subsets.
An element of the Borel subsets is called a Borel set.
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The smallest 20231205121417-sigma_algebra containing (generated) by the open subsets of R is called the Borel σ -algebra or the Borel subsets.
An element of the Borel subsets is called a Borel set.