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

Definition
Let $K$ be a normed field with norm $\left\Vert{\cdot}\right\Vert$.

Let $(a_n)$ be a sequence in $K$.

Then the infinite product $\displaystyle\prod_{n=1}^\infty(1+a_n)$ is absolutely convergent iff $\displaystyle\prod_{n=1}^\infty(1+\Vert a_n\Vert)$ is convergent.