  We calculate the probability distribution of the local density of states
$\nu$ in a disordered one-dimensional conductor or single-mode waveguide,
attached at one end to an electron or photon reservoir. We show that this
distribution does not display a log-normal tail for small $\nu$, but diverges
instead $\propto\nu^{-1/2}$. The log-normal tail appears if $\nu$ is averaged
over rapid oscillations on the scale of the wavelength. There is no such
qualitative distinction between microscopic and mesoscopic densities of states
if the levels are broadened by inelastic scattering or absorption, rather than
by coupling to a reservoir.
