  The restricted-path-integral (RPI) description of a continuous quantum
measurement is rederived starting from the description of an open system by the
Feynman-Vernon influence functional. For this end the total evolution operator
of the compound system consisting of the open system and its environment is
decomposed into the sum of partial evolution operators. Accordingly, the
influence functional of the open system is decomposed into the integral of
partial influence functionals (PIF). If the partial evolution operators or PIF
are chosen in such a way that they decohere (do not interfere with each other),
then the formalism of RPI effectively arises. The evolution of the open system
may then be interpreted as a continuous measurement of this system by its
environment. This is possible if the environment is macroscopic or mesoscopic.
