  Assuming 3-neutrino mixing and massive Majorana neutrinos, we analyze the
possibility of establishing the existence of CP-violation associated with
Majorana neutrinos in the lepton sector i) by measuring of the effective
Majorana mass |<m>| in neutrinoless double beta-decay with a sufficient
precision and ii) by measuring of, or obtaining a stringent upper limit on, the
lightest neutrino mass m1. Information on m1 can be obtained in the tritium
beta decay experiment KATRIN and from astrophysical and cosmological
observations. Proving that the indicated CP-violation takes place requires, in
particular, a relative experimental error on the measured value of |<m>| not
bigger than 20 %, a ``theoretical uncertainty'' in the value of |<m>| due to an
imprecise knowledge of the corresponding nuclear matrix elements smaller than a
factor of 2, a value of tan^2 theta_(solar) larger than 0.55, and values of the
relevant Majorana CP-violating phases typically within the intervals of (Pi/2 -
3 Pi/4) and (5Pi/4 - 3Pi/2).
