Borel Sigma-Algebra

The smallest sigma-algebra on a topological space generated by its open sets (equivalently by its closed sets or by a base of the topology), whose elements are called Borel sets and which provides the minimal measurable structure compatible with the topology.

The sigma-algebra generated by the open sets of a topological space; its members are called Borel sets and are all sets that can be formed from open sets by countable unions, countable intersections and complements.