Jordan measure

In mathematics, a Jordan measure is a generalization of length and area to arbitrary sets of points. It's a rule that assigns a non-negative number to a set, where the sum of the parts equals the whole. For a set to have a Jordan measure, its inner and outer measures must be equal. The outer measure is the lowest possible area of elementary rectangular sets containing the given set, while the inner measure is the highest possible area of such sets contained within the region.1

However, many important sets, like the rational numbers between zero and one, are not Jordan measurable because they cannot be covered by a finite collection of intervals with a greatest lower bound. This limitation led to the development of other measure concepts, such as the Lebesgue measure, which can handle more complex sets.12