Definition:Absolute Convergence of Product

Complex Numbers
Let $\sequence {a_n}$ be a sequence in $\C$.

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

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

Also presented as
The product $\ds \prod_{n \mathop = 1}^\infty a_n$ is absolutely convergent $\ds \prod_{n \mathop = 1}^\infty \paren {1 + \size {a_n - 1} }$ is convergent.

Also see

 * Definition:Convergent Product
 * Absolutely Convergent Product is Convergent
 * Definition:Uniform Absolute Convergence of Product