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We present a detailed analysis of the set theoretical proof of Wigner for Bell type inequalities with the following result. Wigner introduced a crucial assumption that is not related to Einstein's local realism, but instead, without justification, to the existence of certain joint probability measures for possible and actual measurement outcomes of Einstein-Podolsky-Rosen (EPR) experiments. His conclusions about Einstein's local realism are, therefore, not applicable to EPR experiments and thedoi:10.4236/jmp.2017.81005 fatcat:mwknjommqjhyblq2njnrq32saa