  Lorentz invariance is a well known fundamental concept of special relativity
but its violation is predicted by some variations of quantum gravity, string
theory, and some alternatives to general relativity. We study neutrino
oscillation at the presence of the Lorentz invariance violation in vacuum,
normal and nuclear media. It is shown that for very high energy neutrinos the
neutrino oscillations due to mass difference is suppressed and its contribution
to the conversion probability is negligibly small, but the contribution of the
Lorentz invariance violation term is not zero. This means that the observation
of very high energy neutrino oscillations may be a signal of the discreteness
of space and Lorentz invariance violation.
