The effect of the electron-phonon interaction on the density of one-electron states in a metal is discussed in consistence with electric conductivity. By the use of the same Hamiltonian and the same approximation as in Bardeen's theory of resistivity, one obtains the electron mass shift δm/m = 0.32 for sodium in good agreement with the experimental data on specific heat. Based on Eliashberg's formalism, on the other hand, it is shown that the bare electron mass appears in static conductivity and anomalous skin effect. It is suggested that the electron mass is frequency-dependent in the infrared region.