# On the Volume of Compact matrix Lie groups

When we define the volume of a compact matrix lie group (subgroup of $M_n(C)$) by viewing it as a subspace of $R^{n^{2}}$ and applying the usual Lebesgue measure, what's the volume of SO(n), SU(n), Sp(n) and...?

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SO(n) is a compact manifold of dimension $n(n-1)/2$ in $\mathbb R^{n^2}$. It follows that its $n^2$-dimensional Lebesgue measure is $0$. The same argument applies to the other examples.