  We investigate the quantum Zeno effect in the case of electron tunneling out
of a quantum dot in the presence of continuous monitoring by a detector. It is
shown that the Schr\"odinger equation for the whole system can be reduced to
Bloch-type rate equations describing the combined time-development of the
detector and the measured system. Using these equations we find that continuous
measurement of the unstable system does not affect its exponential decay to a
reservoir with a constant density of states. The width of the energy
distribution of the tunneling electron, however, is not equal to the inverse
life-time -- it increases due to the decoherence generated by the detector. We
extend the analysis to the case of a reservoir described by an energy dependent
density of states, and we show that continuous measurement of such quantum
systems affects both the exponential decay rate and the energy distribution.
The decay does not always slow down, but might be accelerated. The energy
distribution of the tunneling electron may reveal the lines invisible before
the measurement.
