Remark 3

Tag 08R5, permanent. Cite it as [Bourbaki, Tag 08R5].

Integration, IV, p. 25, § 3. LP spaces

A Cauchy sequence $(f_n)$ in $\mathscr{L}_F^p$ can be such that the sequence $(f_n(x))$ is not convergent at any point of $X$ (Exer. 1).

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

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