The Energy and Zenith Angle Distribution of Upward Going Muons and Neutrino Oscillations

The energy and zenith angle distribution of neutrino induced, upward going muons can give direct information on the presence of $\nu$--oscillations in precisely the range of parameters suggested as a solution of the atmospheric neutrino problem. We discuss here the uncertainties in the theoretical prediction. The shape of the zenith angle distribution of the muon flux is quite insensitive to modifications of the theoretical input and is a good probe for the existence of neutrino oscillations. We conclude that the existing data sample on $\nu$--induced muons has the statistical power to confirm or refute the $\nu$--oscillation solution of the atmospheric neutrino problem.