Definition 1

Tag 0C0N, permanent. Cite it as [Bourbaki, Tag 0C0N].

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

An infinite product of complex numbers, with general factor $1 + u_n$ , is said to be absolutely convergent if the product with general factor $1 + |u_n|$ is convergent (or, equivalently, if the series with general term $|u_n|$ is convergent).

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

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