Bourbaki

Proposition 1

Tag 08P5, permanent. Cite it as [Bourbaki, Tag 08P5].

Integration, chapter IV, § 1. Upper integral of a positive function

For every finite real number α>0\alpha > 0 and every function f∈J+f \in \mathscr{J}_+,

μ∗(αf)=αμ∗(f). \mu^*(\alpha f) = \alpha \mu^*(f).

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

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Cites

Nothing.

Transcribed from the printed volume. Not translated.