In mathematics, a measurable space or Borel space[1] is a basic object in measure theory. It consists of a set and a σ-algebra, which defines the subsets that will be measured.
It captures and generalises intuitive notions such as length, area, and volume with a set of 'points' in the space, but regions of the space are the elements of the σ-algebra, since the intuitive measures are not usually defined for points. The algebra also captures the relationships that might be expected of regions: that a region can be defined as an intersection of other regions, a union of other regions, or the space with the exception of another region.
