A Lie Group Point of View in the Continuous Measurements Problem

The idea of continuous measurement asks for the concept of weight function in order for one to be able to properly construct the propagator. The main property of the weight function is its invariance property, which is exploited in present work in connection with the measurements in the phase plane of a harmonic oscillator. The weight functions, as well as the conservation laws, are obtained as joint invariant functions of different realizations of the SL (2R) algebraic structure. It is expected that different aspects of the concept of invariance with respect to SL (2R) group and, possibly, some other groups, have a fundamental ontological character