Corollary 2

Tag 08S2, permanent. Cite it as [Bourbaki, Tag 08S2].

For every function $f \in \mathscr{L}^p_F$ , the numerical function $|f|^p$ is integrable and

N_p(f) = \left( \int |f|^p\, d|\mu| \right)^{1/p}.

This follows at once from the fact that $|f|$ belongs to $\mathscr{L}^p$ (§ 3, No. 5, Prop. 11) and formula (2).

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

Cited by

Nothing.