Definition 2

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

General Topology, chapter III, § 5. Infinite sums in commutative groups

A series defined by a sequence $(x_n)$ is said to be commutatively convergent if, for each permutation $\sigma$ of $\mathbf{N}$ , the series defined by the sequence $(x_{\varphi(n)})$ 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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