Proposition 6

Tag 096M, permanent. Cite it as [Bourbaki, Tag 096M].

Integration, chapter V, § 7. Integration with respect to an induced measure

— Let $\Lambda : t \mapsto \lambda_t$ be a μ-adequate mapping of T into $\mathscr{M}_+(X)$ , where X is a locally compact space that is countable at infinity, and let Y be a locally compact subspace of X. Set $\int \lambda_t d\mu(t) = \nu$ . The mapping $t \mapsto \lambda_t|Y$ of T into $\mathscr{M}_+(Y)$ is then μ-adequate, and

\int (\lambda_t|Y) d\mu(t) = \nu|Y.

Taking into account the identifications in the Scholium, this proposition is a special case of Prop. 7 of §5, No. 4.

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

Cited by

Nothing.

Cites

Prop. 7 of §5, No. 4