Corollary 2

Tag 097I, permanent. Cite it as [Bourbaki, Tag 097I].

Integration, chapter V, § 8. Products of measures

— If a set $A \subset T \times T'$ is ν-integrable, then the section $A(t)$ of $A$ at $t$ is μ′-integrable for almost every $t \in T$ , the function $t \mapsto \mu'(A(t))$ is μ-integrable, and

\nu(A) = \int \mu'(A(t))\, d\mu(t).

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

Cited by

§ 8. Products of measures
Exercise 3, § 8

Cites

Nothing.