Superfluid density of a two-dimensional fluid

It is pointed out the definition for the superfluid density in two dimensions used by Nelson and Kosterlitz is not quite correct. The correct definition is simply rederived and connected with the long-wavelength limit of the dielectric function of the Coulomb gas. Nevertheless, the beautiful result of Nelson and Kosterlitz, that the jump in $\frac{{\rho }_{\mathrm{sf}}}{T_c}$ at the transition temperature is universal, is preserved.