Theorem 1

Tag 0C0K, permanent. Cite it as [Bourbaki, Tag 0C0K].

The family $(1 + u_i)_{i \in I}$ is multipliable in $\mathbf{C}^*$ if and only if the family $(|u_i|)$ is summable in $\mathbf{R}$ .

For each finite subset $J$ of $I$ , put

p_J = \prod_{i \in J} (1 + a_i), \quad s_J = \sum_{i \in J} a_i, \quad \sigma_J = \sum_{i \in J} |a_i|.

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

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