The invariance of this volume element is shown by writing the infinitesimal volume elements $$d\eta$$ and $$d\rho$$
$$d\eta=dq_1.....dq_ndp_1......dp_n$$
$$d\rho=dQ_1.......dQ_ndP_1....dP_n$$
and we know that both of them are related to each other by the absolute value of the determinant of...
