The Lebesgue measure on $\mathbb R^n$ is constructed as follows:
A set $A \subset\mathbb R^n$ is Lebesgue measurable if for every $S\subset \mathbb R^n$, we have the following relation in the Lebesgue outer measure $\lambda^*$: \(\lambda^*(S) = \lambda^*(S\cap A) + \lambda^*(S\setminus A).\)
Wikidata ID: Q827230