Corollary 4

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

Integration, chapter IV, § 6. Convexity inequalities

— Let $F$ be a Banach space, $f$ a function in $\mathscr{L}_F^p$ , and $g$ a numerical function belonging to $\mathscr{L}^q$ ; then, the function $fg$ is integrable and

\left| \int fg\, d\mu \right| \leq \int |fg|\, d|\mu| \leq N_p(f) N_q(g).

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

Cited by

Definition 1, § 5

Cites

Nothing.