(i) | $X = \prod_{j \in J} X_j$ and $\mathcal{F} = \prod_{j \in J} \mathcal{F}_j$ are each a D326: Cartesian product |

(ii) | $\mathcal{P}_{\mathsf{cofinite}}(J)$ is the D2200: Set of cofinite sets in $J$ |

**set of measurable cylinder sets**in $X$ with respect to $M = \{ M_j \}_{j \in J}$ is the D11: Set \begin{equation} \left\{ \prod_{j \in J} E_j \subseteq \mathcal{F} \mid \exists \, I \in \mathcal{P}_{\mathsf{cofinite}}(J) : \forall \, i \in I : E_i = X_i \right\} \end{equation}