Corollary 1

Tag 08R8, permanent. Cite it as [Bourbaki, Tag 08R8].

Integration, chapter IV, § 3. LP spaces

— Let $a'$ be a continuous linear form on $F$ ; if $f \in \mathscr{L}_F^p$ , the numerical function $x \mapsto \langle f(x), a' \rangle$ **(denoted by $\langle f, a' \rangle$ )* belongs to* $\mathscr{L}^p$ .

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

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