Derivation of the rule for probabilities in a general quantum mechanical measurement

The quantum-mechanical rule for probabilities, in its most general form of positive-operator valued measure (POVM), is shown to be a consequence of the environment-assisted invariance (envariance) idea suggested by Zurek [1], being completed by Gleason's theorem. This provides also a method for derivation of the Born rule. Report is based on the paper [2].