Definition:Product of Measurable Spaces/Binary Case

Definition
Let $\struct {X_1, \Sigma_1}$ and $\struct {X_2, \Sigma_2}$ be measurable spaces.

The product of $\struct {X_1, \Sigma_1}$ and $\struct {X_2, \Sigma_2}$ is the measurable space:


 * $\struct {X_1 \times X_2, \Sigma_1 \otimes \Sigma_2}$

where $\Sigma_1 \otimes \Sigma_2$ denotes the product $\sigma$-algebra of $\Sigma_1$ and $\Sigma_2$.