  The X-ray luminosities of the Einstein Extended Medium Sensitivity Survey
(EMSS) clusters of galaxies with redshifts 0.3<z<0.6 are remeasured using ROSAT
PSPC data. It is found that the new luminosities are on average 1.18 +/- 0.08
times higher than previously measured but that this ratio depends strongly on
the X-ray core radii we measure. For the clusters with small core radii, in
general we confirm the EMSS luminosities, but for clusters with core radii >250
kpc (the constant value assumed in the EMSS), the new luminosities are 2.2 +/-
0.15 times the previous measurements. The X-ray luminosity function (XLF) at
0.3<z<0.6 is recalculated and is found to be consistent with the local XLF. The
constraints on the updated properties of the 0.3<z<0.6 EMSS sample, including a
comparison with the number of clusters predicted from local XLFs, indicate that
the space density of luminous, massive clusters has either not evolved or has
increased by a small factor ~2 since z=0.4. The implications of this result are
discussed in terms of constraints on the cosmological parameter Omega_0.
