  We study one-dimensional random Jacobi operators corresponding to strictly
ergodic dynamical systems. In this context, we characterize the spectrum of
these operators by non-uniformity of the transfer matrices and the set where
the Lyapunov exponent vanishes. Adapting this result to subshifts satisfying
the so-called Boshernitzan condition, it turns out that the spectrum is
supported on a Cantor set with Lebesgue measure zero. This generalizes earlier
results for Schr\"odinger operators.
