Jordan Measure

Let the set $M$ correspond to a bounded, Nonnegative function $f$ on an interval $0\leq f(x) \leq c$ for $x\in [a,b]$. The Jordan measure, when it exists, is the common value of the outer and inner Jordan measures of $M$.

The outer Jordan measure is the greatest lower bound of the areas of the covering of $M$, consisting of finite unions of Rectangles. The inner Jordan measure of $M$ is the difference between the Area $c(a-b)$ of the Rectangle $S$ with base $[a,b]$ and height $c$, and the outer measure of the complement of $M$ in $S$.

References

Shenitzer, A. and Steprans, J. ``The Evolution of Integration.'' Amer. Math. Monthly 101, 66-72, 1994.