ABSTRACT
Observable dynamical quantities are described by Hermitean operators, and in the early days of quantum mechanics the correspondence was believed to be one-to-one. It was assumed that (i) every observable can be related to some Hermitean operator and (ii) every Hermitean operator corresponds to one observable. The arguments concerning the difference between proper and improper mixtures are conceived of for the benefit of the physicists with a "realist" turn of mind who, prima facie, would tend to consider that, quite on the contrary, the statement in question is meaningful and true. Two ensembles are said to be different with respect to some observable A if the statistical frequencies of the prospective measurement outcomes on observable A are different on the two ensembles. Also, two ensembles are said to be different if there exists at least one observable A with respect to which they are different.
