Corollary
Tag 09AF, permanent. Cite it as [Bourbaki, Tag 09AF].
Integration, chapter VI, § 2. Vectorial measures . "
— If the space F is finite-dimensional, then every vectorial measure m with values in F is majorizable. In order that a numerical function be essentially integrable for m, it is necessary and sufficient that it be essentially integrable for |m| (where |x| denotes any norm on F).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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