Off-diagonal terms in a determinant always occur in pairs, and such products are of order . Thus Hence we have plus terms of order . If we now take the limit we get exactly where we used Liouville's theorem. Hence the flow is incompressible . This is the great advantage of phase space.
Compressible liquids are hard to deal with, but phase flow is fortunately incompressible.
It is like a piece of rubber that can be stretched and deformed but has to keep the same volume. The volume cannot rearrange itself internally in a discontinuous manner.