ABSTRACT
This chapter investigates quantum continuous measurements from the point of view of their group-theoretical structure. There are two sources of a group-theoretical structure. One is that evolution develops continuously in time. Another source of group-theoretical structure is the equivalence of different measurement outputs. This equivalence can be described by the transverse group transforming alternative outputs into each other. To treat the group structure connected with time evolution, the notation has to be made more detailed, with explicit marking of the initial and final instants. A quantum system under continuous measurement exhibits evolution of a quite new type, having classical and quantum features simultaneously. The Galilean type semigroups are in fact very similar in the two cases, but the representations arising in describing the evolution must be more complicated in the presence of a measurement.
