Theorem 2

Tag 08R1, permanent. Cite it as [Bourbaki, Tag 08R1].

Integration, IV, p. 24, § 3. LP spaces

The space $\mathscr{L}_\mathbf{F}^p$ is complete; the space $L_\mathbf{F}^p$ is a Banach space.

In the space $L_\mathbf{F}^p$ , the norm $N_p(\tilde{\mathbf{f}})$ of a class is again denoted $\| \tilde{\mathbf{f}} \|_p$ .

Th. 2 can be sharpened as follows:

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

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