  We present results from the analysis of cosmic microwave background (CMB),
large scale structure (galaxy redshift survey) and X-ray galaxy cluster (baryon
fraction and X-ray luminosity function) data, assuming a geometrically flat
cosmological model and allowing for tensor components and a non-negligible
neutrino mass. From a combined analysis of all data, assuming three degenerate
neutrinos species, we measure a contribution of neutrinos to the energy density
of the universe, Omega_nu h^2=0.0059^{+0.0033}_{-0.0027} (68 per cent
confidence limits), with zero falling on the 99 per cent confidence limit. This
corresponds to ~4 per cent of the total mass density of the Universe and
implies a species-summed neutrino mass \sum_i m_i =0.56^{+0.30}_{-0.26} eV, or
m_nu~0.2 eV per neutrino. We examine possible sources of systematic uncertainty
in the results. Combining the CMB, large scale structure and cluster baryon
fraction data, we measure an amplitude of mass fluctuations on 8h^{-1} Mpc
scales of sigma_8=0.74^{+0.12}_{-0.07}, which is consistent with measurements
based on the X-ray luminosity function and other studies of the number density
and evolution of galaxy clusters. This value is lower than that obtained when
fixing a negligible neutrino mass (sigma_8=0.86^{+0.08}_{-0.07}). The
combination of CMB, large scale structure and cluster baryon fraction data also
leads to remarkably tight constraints on the Hubble constant,
H_0=68.4^{+2.0}_{-1.4} km/s/Mpc, mean matter density, Omega_m =0.31\pm0.02 and
physical baryon density, Omega_b h^2=0.024\pm0.001, of the Universe.
