  Both active and sterile sub-eV neutrinos can form the cosmic neutrino
background in the early Universe. We consider the beta-decaying (e.g., $^3$H)
and EC-decaying (e.g., $^{163}$Ho) nuclei as the promising targets to capture
relic neutrinos in the laboratory. We calculate the capture rates of relic
electron neutrinos and antineutrinos against the corresponding beta decay or
electron capture (EC) decay backgrounds in the (3+$N_{\rm s}$) flavor mixing
scheme, and discuss the future prospect in terms of the PTOLEMY project. We
stress that such direct measurements of hot DM might not be hopeless in the
long term.
