  We consider {\em non-selective} continuous measurements of a particle
tunneling to a reservoir of finite band-width ($\Lambda$). The particle is
continuously monitored by frequent projective measurements ("quantum
trajectory"), separated by a time-interval $\tau$. A simple analytical
expression for the decay rate has been obtained. For Markovian reservoirs
($\Lambda\to\infty$), no effect of the measurements is found. Otherwise for a
finite $\Lambda$, the decay rate always depends on the measurement time $\tau$.
This result is compared with alternative calculations, with no intermediate
measurements, but when the measurement device is included in the Schr\"odinger
evolution. We found that the detector affects the system by the decoherence
rate ($\Gamma_d$), related to the detector's signal. Although both treatments
are different, the final results become very close for $\tau=2/\Gamma_d$. This
$\tau$ corresponds to the minimal time for which the detector's signal can be
distinguished by an "observer". This indicates a fundamental role of
information in quantum motion and can be used for the extension of the quantum
trajectory method for non-Markovian environments.
