\begin{definition}[Definition:Product of Measurable Spaces/Countable Case]
Let $\sequence {\struct {X_i, \Sigma_i} }_{i \in \N}$ be a sequence of measurable spaces. 
The '''product of $\struct {X_1, \Sigma_1}, \struct {X_2, \Sigma_2}, \ldots$''' is the measurable space:
:$\ds \struct {\prod_{i \mathop = 1}^\infty X_i, \bigotimes_{i \mathop = 1}^\infty \Sigma_i}$
where $\ds \bigotimes_{i \mathop = 1}^\infty \Sigma_i$ denotes the product $\sigma$-algebra of $\Sigma_1, \Sigma_2, \ldots$.
\end{definition}