  One of the broadest concepts of measurement in quantum theory is the
generalized measurement. Another paradigm of measurement--arising naturally in
quantum optics, among other fields--is that of continuous-time measurements,
which can be seen as the limit of a consecutive sequence of weak measurements.
They are naturally described in terms of stochastic processes, or
time-dependent random variables. We show that any generalized measurement can
be decomposed as a sequence of weak measurements with a mathematical limit as a
continuous stochastic process. We give an explicit construction for any
generalized measurement, and prove that the resulting continuous evolution, in
the long-time limit, collapses the state of the quantum system to one of the
final states generated by the generalized measurement, being decomposed, with
the correct probabilities. A prominent feature of the construction is the
presence of a feedback mechanism--the instantaneous choice weak measurement at
a given time depends on the outcomes of earlier measurements. For a generalized
measurement with $n$ outcomes, this information is captured by a real
$n$-vector on an $n$-simplex, which obeys a simple classical stochastic
evolution.
