Definition:Jordan Content

Definition

Let $M \subseteq \R^n$ be a bounded subspace of Euclidean $n$-space.

The Jordan content is defined and denoted as:

$\map m M = \map {m^*} M = \map {m_*} M$

where:

$\map {m^*} M$ denotes the outer Jordan content of $M$

$\map {m_*} M$ denotes the inner Jordan content of $M$

if and only if the two values are equal.

If $\map {m^*} M \ne \map {m_*} M$, then the Jordan content of $M$ is undefined.

Also known as

The Jordan content is 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
• Definition:Inner Jordan Content

• Results about Jordan content can be found here.

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