classical mechanics - The invariant measure on an energy surface of a Hamiltonian system

Consider a Hamiltonian system with a time-independent Hamiltonian $H (p, q )$. By the Liouville theorem, the measure $d^np d^nq $ is conserved.

However, one should also notice that the energy is conserved and the system does not evolve in a space, but on a hypersurface, i.e., the energy surface $E = H(p, q)$.

So, what is the invariant measure on the energy surface, if there exists such a measure at all?