Non-Kolmogorov probability models and modified Bell’s inequality

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Abstract
We analyze the proof of Bell’s inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatics from 1933. We found a (numerical) statistical correction to Bell’s inequality. Such an additional term ε φ on the right-hand side of Bell’s inequality can be considered as a probability invariant of a quantum state φ. This is a measure of nonreproducibility of hidden variables in different runs of experiments. Experiments to verify Bell’s inequality can be considered as just experiments to estimate the constant ε φ . It seems that Bell’s inequality could not be used as a crucial reason to deny local realism. We consider deterministic as well as stochastic hidden variables models.
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