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 $\Sigma_2$.

Sources

• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $13.2$