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In 1970’s Eugene Wigner proposed the new test of Local Realism in inequalities for probabilities (so called Wigner inequalities). After some years professor Bertlmann proposed to consider for this goal the experiments with the neutral kaons systems. All theoretical calculations was prepared for the pure states of entangled kaons pair. But in the real experiments we have the mixing states of pure state of entangled kaons and background. How to change the conditions of Wigner’s inequalities violations if we take into account the existiong of background component? My report will be able to answer this question.