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

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

Let $\sequence{a_n}$ be a sequence in $\mathbb K$.

The infinite product $\displaystyle \prod_{n \mathop = 1}^\infty \paren{1 + a_n}$ is absolutely convergent $\displaystyle \prod_{n \mathop = 1}^\infty \paren{1 + \norm{a_n}}$ is convergent.

Also see

 * Equivalence of Definitions of Absolute Convergence of Product