Remark 1

Tag 0C0P, permanent. Cite it as [Bourbaki, Tag 0C0P].

General Topology, chapter VIII, § 3. Infinite sums and products of complex numbers

The product with general factor $|1 + u_n|$ can be convergent, and indeed absolutely convergent in $\mathbf{R}_i^*$ , without the convergence of the product with general factor $1 + |u_n|$ (see Exercise 4); of course, this cannot happen if all the $u_n$ are real and $> 0$ from a certain index onwards.

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

Cited by

Nothing.

Cites

Exercise 4