Corollary 3
Tag 08UV, permanent. Cite it as [Bourbaki, Tag 08UV].
Integration, chapter IV, § 5. Measurable functions and sets
— If f and g are two measurable mappings of X into a topological vector space F, then f + g and αf are measurable (α any scalar).
The set of measurable mappings of X into a topological vector space F is thus a vector space.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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