\begin{definition}[Definition:Riemannian Volume Form/Definition 2]
Let $\struct {M, g}$ be an oriented $n$-dimensional Riemannian manifold.
Let $T M$ be the tangent bundle of $M$.
Let $\tuple {E_1, \ldots, E_n}$ be a local oriented orthonormal frame of $T M$.
The '''Riemannian volume form''', denoted by $\rd V_g$, is an $n$-form such that:
:$\map {\rd V_g} {E_1, \ldots, E_n} = 1$
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\end{definition}