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 $\ds \prod_{n \mathop = 1}^\infty \paren {1 + a_n}$ is absolutely convergent if and only if $\ds \prod_{n \mathop = 1}^\infty \paren {1 + \norm {a_n} }$ is convergent.

Also see

• Equivalence of Definitions of Absolute Convergence of Product