Corollary

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

General Topology, chapter VII, § 3. Infinite sums in the groups $\mathbf{R}^n$

A family $(x_i)$ of points of $\mathbf{R}^n$ is summable if and only if the set of finite partial sums of the family is bounded in $\mathbf{R}^n$ .

By Theorem 1 and the triangle inequality, this condition is necessary; it is sufficient by the inequality (1) and Theorem 1.

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

Cited by

Nothing.

Cites

Theorem 1