Definition 4.2.1 (Product $\s$-Algebra).label Let $\curl{(X_i,\cali{M}_i)}_{i\in I}$ be measurable spaces, then the product $\s$-algebra $\tprods{}{i\in I}\cali{M}_{i}$ on $\prods{}{i\in I}X_{i}$ is the $\s$-algebra generated by $\curl{\pi_i}_{i\in I}$.