Bourbaki

Proposition 1

Tag 0963, permanent. Cite it as [Bourbaki, Tag 0963].

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

— For every numerical function g⩾0g \geqslant 0 defined on X,

∫∙g dμX=∫Xg dμ \int^\bullet g\,d\mu_X = \int_X g\,d\mu

(cf. §5, No. 3, Example, for the notation ∫X∙\int_X^\bullet).

Taking into account the preceding remarks and (2), the relation (3) follows from Th. 1 of §4.

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

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Cites

Transcribed from the printed volume. Not translated.