How can I compute the Lebesgue measure

Question

Let $\mathcal{X}$ be a tensor whose frontal slices are defined by $X_1=\begin{bmatrix}{1}&{0}\\{0}&{1}\end{bmatrix}$ and $X_2=\begin{bmatrix}{0}&{1}\\{-1}&{0}\end{bmatrix}$. This is a tensor of rank-3 over $\mathbb{R}$ and a rank-2 over $\mathbb{C}$ The rank decomposition over $\mathbb{R}$ is $\mathcal{X}=[A,B,C]$ where $A=\begin{bmatrix}{1}&{0}&{1}\\{0}&{1}&{-1}\end{bmatrix}$, $B=\begin{bmatrix}{1}&{0}&{1}\\{0}&{1}&{1}\end{bmatrix}$ and $C=\begin{bmatrix}{1}&{1}&{0}\\{-1}&{1}&{1}\end{bmatrix}$. Whereas the rank decomposition over $\mathbb{C}$ has the following factor matrices instead: $A=\frac{1}{\sqrt{2}}\begin{bmatrix}{1}&{1}\\{-i}&{i}\end{bmatrix}$, $B=\frac{1}{\sqrt{2}}\begin{bmatrix}{1}&{1}\\{i}&{-i}\end{bmatrix}$ and $C=\begin{bmatrix}{1}&{1}\\{-i}&{i}\end{bmatrix}$. My question is, how can I compute the Lebesgue measure for the tensor above? Thanks!!!