Definition:Jordan Content
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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
- 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