\begin{definition}[Definition:Riemannian Density]
Let $\struct {M, g}$ be an $n$-dimensional Riemannian manifold.
Let $\tuple {E_i}$ be an local orthonormal frame.
Let $\mu$ be a positive smooth density such that:
:$\forall \tuple {E_i} : \map \mu {E_1, \ldots, E_n} = 1$
Then $\mu$ is known as the '''Riemannian density'''.
{{MissingLinks|tensor density}}
{{Research|"for all frames"}}
\end{definition}