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