  The universality of the continuum limit and the applicability of renormalized
perturbation theory are tested in the SU(2) lattice gauge theory by computing
two different non-perturbatively defined running couplings over a large range
of energies. The lattice data (which were generated on the powerful APE
computers at Rome II and DESY) are extrapolated to the continuum limit by
simulating sequences of lattices with decreasing spacings. Our results confirm
the expected universality at all energies to a precision of a few percent. We
find, however, that perturbation theory must be used with care when matching
different renormalized couplings at high energies.
