Proposition 9

Tag 08PH, permanent. Cite it as [Bourbaki, Tag 08PH].

Integration, chapter IV, § 1. Upper integral of a positive function

For Lebesgue measure on $\mathbf{R}$ , the outer measure of an open set in $\mathbf{R}$ is equal to the sum of the lengths of its connected components.

Note in particular that if $G$ is an open set in $\mathbf{R}$ such that $\mu^*(G) = 0$ , then $G$ is empty.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Remark, § 1
Example, § 4

Cites

Nothing.