We discuss fluctuations in the measurement process and how these fluctuatio
ns are related to the dissipational parameter characterizing quantum dampin
g or decoherence. On the example of the measuring current of the variable-b
arrier or QPC problem we discuss the extra noise or fluctuation connected w
ith the different possible outcomes of a measurement. This noise has an enh
anced short time component which could be interpreted as due to "telegraph
noise" or "wavefunction collapses". Furthermore, the parameter giving the s
trength of this component is related to the parameter giving the rate of da
mping or decoherence. (C) 1999 Elsevier Science B.V. All rights reserved.