THIS WORK CONTAINSAN ANALYSIS OF SOME OF THE FUNDAMENTAL PRINCIPLES UNDERLAYING THE CONSTRUTION OF OPERATORS IN QUANTUM MECHANICS. FACH OPERATOR IS ASSOCIATED TO A PROJECTION OPERATOR AND THESE PROJECTION OPERATORS ARE SHOWS TO FULFIL A SET OF PROPERTIES FORMALLY INDENTICAL TO THOSE OF A PROBABILITY FIELD.IT IS SHOWN THAT, BY THE INTRODUCTION OFA MEASURE IN CONFIGURATION SPACE IT IS POSSIBLE TO OBTAIN COMPLETE SETS OF COMMUTING OBSERVABLES HAVING, WITHIN LIMITS, PREASIGNED SPECTRA. THE INTRODUCTION OF NEW OPERATORS BY CONSIDERATION OF THE GROUPS EXPRESSING THE SYMMETRIES OF THE SYSTEM, IS DISCUSSED.