Lower mass limits for particles constituting the dark matter in galaxy halos can be derived from considerations of the initial and final phase space distribution. In the case of massive neutrinos, Tremaine and Gunn (1979) pointed out that the initial fine-grained occupation number of cosmological neutrinos and therefore the final coarse-grained phase space occupation, is less than 0.5. From this they were able to show that if the final neutrino distribution is an isothermal sphere, one can put lower limits on the neutrino mass from assumptions about the core radius of the neutrino sphere.