Liouville's theorem states that the `natural' 2-from is preserved under the Hamiltonian flow. Apparently this leads to an invariant measure $\mu$ as follows

\begin{equation} d\mu = \frac{d\sigma}{|| \nabla H ||} \end{equation} where $H$ is the Hamiltonian and $d\sigma$ an infinitesimal standard volume element. I have never quite understood how one arrives at this and why you cannot consider the 2-form of the Hamiltonian as a measure. The books I have seen up to now seem to label this as trivial but I do not see the connection. Could anybody explain this?

Thanks in advance.