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We show that even the smallest neutrino mass consistent with theSuper--Kamiokande data is relevant for cosmological models of structureformation and cosmic microwave background (CMB) anisotropies, provided that arelic neutrino asymmetry exists. We calculate the precision with which a 0.07eV neutrino mass could be extracted from CMB anisotropy and large-scalestructure data by the future Planck satellite and Sloan Digital Sky Survey. Wefind that such a mass can be detected, assuming a large relic neutrinoasymmetry still allowed by current experimental data. This measurement of theabsolute value of the neutrino mass would be crucial for our understanding ofneutrino models.Comment: 8 pages, 2 PS figures, version to be publishe

Cosmological measurement of neutrino mass in the presence of leptonic asymmetry