Let the set correspond to a bounded, Nonnegative function on an interval for . The Jordan measure, when it exists, is the common value of the outer and inner Jordan measures of .
The outer Jordan measure is the greatest lower bound of the areas of the covering of , consisting of finite unions of Rectangles. The inner Jordan measure of is the difference between the Area of the Rectangle with base and height , and the outer measure of the complement of in .
Shenitzer, A. and Steprans, J. ``The Evolution of Integration.'' Amer. Math. Monthly 101, 66-72, 1994.