Bourbaki

Proposition 3

Tag 092J, permanent. Cite it as [Bourbaki, Tag 092J].

Integration, V, p. 43, § 5. Measures defined by numerical densities

For every numerical function f⩾0f \geqslant 0 defined on TT,

∫∙f dν=∫∙(fg) dμ. \int^\bullet f \, d\nu = \int^\bullet (f g) \, d\mu .

This follows from Th. 1 of §4, No. 2.

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.