Remark 2

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

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

In general, the space $\mathscr{F}_\mathbf{F}^p$ is distinct from its subspace $\mathscr{L}_\mathbf{F}^p$ (§4, Exer. 8).

Def. 2 immediately yields the following criterion:

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

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