Definition 5

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

Integration, chapter IV, § 4. Integrable functions and sets

— A real-valued function $\lambda$ defined on a clan $\Phi$ of subsets of a set $A$ is said to be additive if, for every pair $M, N$ of disjoint sets belonging to $\Phi$ , $\lambda(M \cup N) = \lambda(M) + \lambda(N)$ .

It follows in particular from this definition that $\lambda(\varnothing) = 0$ .

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

Cited by

Proposition 18, § 4

Cites

Nothing.