Exercise 18, § 7

Let $(1 + u_i)$ be a family of real numbers all belonging to the interval $[0, +\infty[$ (resp. ]$0, +\infty$]). Then the family $(1 + u_i)$ is multipliable in $\mathbf{R}$ if and only if one of the following conditions is satisfied: a) At least one of the numbers $1 + u_i$ is equal to $0$ (resp. $+\infty$). b) The family $u_i$ is summable in $\overline{\mathbf{R}}$.