Non-Kolmogorov probability models and modified Bell's inequality

We analyze the proof of Bell's inequality and demonstrate that this inequal ity is related to one particular model of probability theory, namely Kolmog orov measure-theoretical axiomatics from 1933. We found a (numerical) stati stical correction to Bell's inequality. Such an additional term epsilon(phi ) on the right-hand side of Bell's inequality can be considered as a probab ility invariant of a quantum state phi. This is a measure of nonreproducibi lity of hidden variables in different runs of experiments. Experiments to v erify Bell's inequality can be considered as just experiments to estimate t he constant epsilon(phi). It seems that Bell's inequality could not be used as a crucial reason to deny local realism. We consider deterministic as we ll as stochastic hidden variables models. (C) 2000 American Institute of Ph ysics. [S0022-2488(00)01504-8].