  We give an explicit axiomatic formulation of the quantum measurement theory
which is free of the projection postulate. It is based on the generalized
nondemolition principle applicable also to the unsharp, continuous-spectrum and
continuous-in-time observations. The "collapsed state-vector" after the
"objectification" is simply treated as a random vector of the a posteriori
state given by the quantum filtering, i.e., the conditioning of the a priori
induced state on the corresponding reduced algebra. The nonlinear
phenomenological equation of "continuous spontaneous localization" has been
derived from the Schroedinger equation as a case of the quantum filtering
equation for the diffusive nondemolition measurement. The quantum theory of
measurement and filtering suggests also another type of the stochastic equation
for the dynamical theory of continuous reduction, corresponding to the counting
nondemolition measurement, which is more relevant for the quantum experiments.
