Corollary 2

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

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

If $(x_\lambda)_{\lambda \in L}$ and $(y_\mu)_{\mu \in M}$ are two summable families of points of $\mathbf{R}^n$ , then the family $(x_\lambda | y_\mu)$ (cf. Chapter VI, § 2, no. 2) is summable in $\mathbf{R}$ , and we have

\sum_{(\lambda, \mu) \in L \times M} (x_\lambda | y_\mu) = \left( \sum_{\lambda \in L} x_\lambda \middle| \sum_{\mu \in M} y_\mu \right).

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

Cited by

Nothing.

Cites

Chapter VI, § 2, no. 2