Definition 4

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

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

Let $\mu$ be a positive measure on $X$ ; for every subset $A$ of $X$ , the upper integral $\mu^*(\varphi_A)$ is called the outer measure of $A$ (with respect to the measure $\mu$ ) and is denoted $\mu^*(A)$ .

The outer measure of a set is thus a number $\geq 0$ , finite or equal to $+\infty$ , that, for an open set, coincides with the outer measure defined in Def. 2 of No. 2.

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

Cited by

Nothing.

Cites

Def. 2