  We establish connections between the requirement of measurability of a
probability space and the principle of complimentarity in quantum mechanics. It
is shown that measurability of a probability space implies the dependence of
results of quantum measurement not only on the properties of a quantum object
under consideration, but also on the classical characteristics of the measuring
device which is used. We show that if one takes into account the requirement of
measurability in a quantum case, the Bell inequality does not follow from the
hypothesis about the existence of an objective reality.
