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.