Definition 3

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

Integration, IV, p. 50, § 4. Integrable functions and sets

A nonempty set $\Phi$ of subsets of a set $A$ is said to be a clan if there exists an algebra $\mathscr{A}$ (over $\mathbf{R}$ ) consisting of real-valued functions defined on $A$ , such that the relations $M \in \Phi$ and $\varphi_M \in \mathscr{A}$ are equivalent.

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

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