  Feynman proposed a postulate or a method of quantization in his celebrated
paper in 1948. Applying Feynman's postulate to temporally continuous quantum
measurements of the positions of particles, Mensky proposed the restricted
Feynman path integrals for continuous quantum measurements after
phenomenological considerations. Our aim in the present paper is to give a
rigorous proof that Mensky's restricted Feynman path integrals emerge out of
the Feynman's postulate under a simple approximation. In addition, it is proved
that the restricted Feynman path integrals emerge out of von Neumann's
postulate on instantaneous measurements as well as Feynman's postulate. The
quantum systems that we study include spin systems. These results are applied
to formulations of the multi-split experiments, the quantum Zeno and the
Aharanov-Bohm effects.
