  Within the framework of three-neutrino and four-neutrino scenarios that can
describe the results of the LSND experiment, we consider the capabilities of
short baseline neutrino oscillation experiments at a neutrino factory. We find
that, when short baseline ($L \alt 100$ km) neutrino factory measurements are
used together with other accelerator-based oscillation results, the complete
three-neutrino parameter space can best be determined by measuring the rate of
$\nu_e \to \nu_\tau$ oscillations, and measuring CP violation with either
$\nu_e \to \nu_\mu$ or $\nu_\mu \to \nu_\tau$ oscillations (including the
corresponding antineutrino channels). With measurements of CP violation in both
$\nu_e \to \nu_\mu$ and $\nu_\mu \to \nu_\tau$ it may be possible to
distinguish between the three- and four-neutrino cases.
