  We present comparative probabilistic analysis of the
Greenburger-Horne-Zeilinger paradox in the frameworks of Kolmogorov's
(measure-theoretical) and von Mises' (frequency) models of the probability
theory. This analysis demonstrated that the GHZ paradox is merely a consequence
of the use of Kolmogorov's probabilistic model. By using von Mises' frequency
approach we escape the contradiction between the local realism and quantum
formalism. The frequency approach implies automatically contextual
interpretation of quantum formalism: different collectives induce different
probability distributions. On the other hand, the formal use of Kolmogorov's
model implies the identification of such distributions with one abstract
Kolmogorov measure. In the measure-theoretical approach we can escape the
paradox, if we do not suppose that probability distributions corresponding to
different settings of measurement devices are equivalent. We discuss the
connection between equivalence/singularity dichotomy in measure theory and the
existence of compatible and noncompatible observables.
