  We consider Tikhonov regularization of control-constrained optimal control
problems. We present new a-priori estimates for the regularization error
assuming measure and source-measure conditions. In the special case of
bang-bang solutions, we introduce another assumption to obtain the same
convergence rates. This new condition turns out to be useful in the derivation
of error estimates for the discretized problem. The necessity of the just
mentioned assumptions to obtain certain convergence rates is analyzed. Finally,
a numerical example confirms the analytical findings.
