Let $\mathbb{R}^N$ be a D816: Euclidean real Cartesian product.
Let $\mathsf{Vol}$ be the D1738: Euclidean real volume function on $\mathbb{R}^N$.
Let $\mathsf{Vol}$ be the D1738: Euclidean real volume function on $\mathbb{R}^N$.
Then
\begin{equation}
\forall \, x \in \mathbb{R}^N : \mathsf{Vol} \Big( \prod_{n = 1}^N [x_n, x_n] \Big) = \mathsf{Vol}(\{ x \}) = 0
\end{equation}