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A new X-ray selected and X-ray flux-limited galaxy cluster sample ispresented. Based on the ROSAT All-Sky Survey the 63 brightest clusters withgalactic latitude |bII| >= 20 deg and flux fx(0.1-2.4 keV) >= 2 * 10^{-11}ergs/s/cm^2 have been compiled. Gravitational masses have been determinedutilizing intracluster gas density profiles, derived mainly from ROSAT PSPCpointed observations, and gas temperatures, as published mainly from ASCAobservations, assuming hydrostatic equilibrium. This sample and an extendedsample of 106 galaxy clusters is used to establish the X-rayluminosity--gravitational mass relation. From the complete sample the galaxycluster mass function is determined and used to constrain the mean cosmicmatter density and the amplitude of mass fluctuations. Comparison toPress--Schechter type model mass functions in the framework of Cold Dark Mattercosmological models and a Harrison--Zeldovich initial density fluctuationspectrum yields the constraints OmegaM = 0.12^{+0.06}_{-0.04} and sigma8 =0.96^{+0.15}_{-0.12} (90% c.l.). Various possible systematic uncertainties arequantified. Adding all identified systematic uncertainties to the statisticaluncertainty in a worst case fashion results in an upper limit OmegaM < 0.31.For comparison to previous results a relation sigma8 = 0.43 OmegaM^{-0.38} isderived. The mass function is integrated to show that the contribution of massbound within virialized cluster regions to the total matter density is small,i.e., OmegaCluster = 0.012^{+0.003}_{-0.004} for cluster masses larger than6.4^{+0.7}_{-0.6} * 10^{13} h_{50}^{-1} Msun.

The Mass Function of an X‐Ray Flux–limited Sample of Galaxy Clusters