From the Press-Schechter mass function and the empirical X-ray cluster luminosity-temperature (L-T) relation, we construct an X-ray cluster luminosity function that can be applied to the growing number of high-redshift, X-ray cluster luminosity catalogs to constrain cosmological parameters. In this paper, we apply this luminosity function to the Einstein Medium Sensitivity Survey (EMSS) and the ROSAT Brightest Cluster Sample (BCS) luminosity function to constrain the value of Ωm. In the case of the EMSS, we find a factor of 4-5 fewer X-ray clusters at redshifts above z = 0.4 than below this redshift at luminosities above LX = 7 × 1044 ergs s-1 (0.3-3.5 keV), which suggests that the X-ray cluster luminosity function has evolved above L(Black star). At lower luminosities, this luminosity function evolves only minimally, if at all. Using Bayesian inference, we find that the degree of evolution at high luminosities suggests that Ωm = 0.96+0.36-0.32, given the best-fit L-T relation of Reichart, Castander, & Nichol. When we account for the uncertainty in how the empirical L-T relation evolves with redshift, we find that Ωm ≈ 1.0 ± 0.4. However, it is unclear to what degree systematic effects may affect this and similarly obtained results
