Definition:Jordan Content

Definition

Let $M$ be a bounded subspace of Euclidean space.

Let $S$ be an orthotope enclosing $M$.

If the outer Jordan content $\map {m^*} M = \map V S - \map {m^*} {S \setminus M}$, then it is the Jordan content.

That is, if the outer Jordan content equals the difference between the content of $S$ and the outer Jordan content of the relative complement of $M$ in $S$.

If that equality does not hold, then the Jordan content of $M$ does not exist.

Also known as

Often referred to as the Jordan measure, but this is a misnomer as it is does not constitute a measure.

Also see

• Definition:Outer Jordan Content

Source of Name

This entry was named for Marie Ennemond Camille Jordan.

Sources

• 1994: A. Shenitzer and J. Steprans: The Evolution of Integration (Amer. Math. Monthly Vol. 101, no. 1: pp. 66 – 72)  www.jstor.org/stable/2325128

• Derwent, John. "Jordan Measure." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/JordanMeasure.html