Bourbaki

Proposition 2

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

Integration, V, p. 41, § 5. Measures defined by numerical densities

Let θ\theta be a complex measure, and uu a locally θ\theta-integrable complex function; then

∣u⋅θ∣=∣u∣⋅∣θ∣. |u \cdot \theta| = |u| \cdot |\theta|.

We begin with an auxiliary result:

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

Cited by

Cites

Nothing.

Transcribed from the printed volume. Not translated.