Corollary

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

Let $(x_i)_{i \in I}$ be a summable family of finite numbers $\geq 0$ in $\mathbf{R}$ . If $H$ is any subset of $I$ , we have

\sum_{i \in H} x_i \leq \sum_{i \in I} x_i,

and equality holds only if

x_i = 0

for all

i \in \complement H

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

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