Borel Set

A Borel set is a type of set that can be formed from open or closed sets through processes like countable unions, intersections, and complements. Think of it as a collection of points or intervals that can be built step-by-step starting with simple open or closed shapes, using well-defined operations. Borel sets are fundamental in measure theory and probability because they provide a rigorous way to define and work with measurable sets within spaces like the real number line, ensuring the tools of calculus and probability apply consistently.