We give an explicit axiomatic formulation of the quantum measurement t
heory which is free of the projection postulate. It is based on the ge
neralized nondemolition principle applicable also to the unsharp, cont
inuous-spectrum and continuous-in-time observations. The ''collapsed s
tate-vector'' after the ''objectification'' is simply treated as a ran
dom vector of the a posteriori state given by the quantum filtering, i
.e., the conditioning of the a priori induced state on the correspondi
ng reduced algebra. The nonlinear phenomenological equation of ''conti
nuous spontaneous localization'' has been derived from the Schrodinger
equation as a case of the quantum filtering equation for the diffusiv
e nondemolition measurement. The quantum theory of measurement and fil
tering suggests also another type of the stochastic equation for the d
ynamical theory of continuous reduction, corresponding to the counting
nondemolition measurement, which is more relevant for the quantum exp
eriments.