Proposition 1

Tag 0C0I, permanent. Cite it as [Bourbaki, Tag 0C0I].

General Topology, chapter VIII, § 3. Infinite sums and products of complex numbers

If $(u_\lambda)_{\lambda \in L}$ and $(v_\mu)_{\mu \in M}$ are two summable families of complex numbers, then the family $(u_\lambda v_\mu)_{(\lambda, \mu) \in L \times M}$ is summable and we have

\sum_{(\lambda, \mu) \in L \times M} u_\lambda v_\mu = \left( \sum_{\lambda \in L} u_\lambda \right) \left( \sum_{\mu \in M} v_\mu \right).

We leave it to the reader to state the corresponding result for quaternions.

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

Cited by

Nothing.

Cites

Nothing.