Definition:Absolute Convergence of Product/General Definition/Definition 1

Definition
Let $\struct {\mathbb K, \size{\,\cdot\,}}$ be a valued field.

Let $\left\langle{a_n}\right\rangle$ be a sequence in $\mathbb K$.

The infinite product $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + a_n}\right)$ is absolutely convergent $\displaystyle \prod_{n \mathop = 1}^\infty \left({1 + \left\vert{a_n}\right\vert}\right)$ is convergent.

Also see

 * Equivalence of Definitions of Absolute Convergence of Product