  We show that, under the long-tailedness of the densities of normalized L\'evy
measures, the densities of infinitely divisible distributions on the half line
are subexponential if and only if the densities of their normalized L\'evy
measures are subexponential. Moreover, we prove that, under a certain
continuity assumption, the densities of infinitely divisible distributions on
the half line are subexponential if and only if their normalized L\'evy
measures are locally subexponential.
