Let $J$ be a D11: Set.
Let $\mathbb{R}$ be the D282: Set of real numbers.
The real cartesian product with respect to $J$ is the D11: Set \begin{equation} \mathbb{R}^J : = \prod_{j \in J} \mathbb{R} : = \{ x \mid x : J \to \mathbb{R} \} \end{equation}