The Borel σ-algebra is a collection of sets that is fundamental in the field of measure theory and probability. It is generated from open sets in a topological space, such as the real numbers ℝ. This means it includes all open sets, closed sets, countable unions, countable intersections, and complements of these sets. In practical terms, the Borel σ-algebra allows mathematicians to define measurable sets and functions, which are essential for integrating and analyzing data. It provides a framework for understanding concepts like probability measures, making it crucial for fields such as statistics and quantum mechanics.