Corollary

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

General Topology, chapter IV, § 7. Infinite sums and products of real numbers

The product $\prod (1 + u_i)$ [resp. $\prod (1 - u_i)$ ] of numbers $\geq 1$ (resp. $> 0$ and $\leq 1$ ) is equal to $+ \infty$ (resp. 0) if and only if $\sum u_i = + \infty$ .

For if $\sum u_i$ is finite then $\prod (1 + u_i)$ and $\prod (1 - u_i)$ are in $\mathbf{R}^*$ , and conversely (no. 4, Theorem 4).

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

Cited by

Nothing.

Cites

no. 4, Theorem 4