This article identifies a series of foundational mathematical and logical inconsistencies within John Bell’s 1964 formulation and demonstrates that the core discrepancy in Bell’s framework arises from an implicit and unjustified data-mapping assumption which treats the discrete, binary-valued random functions of one expectation value integral as directly equivalent to the continuous, real-valued integrand of another expectation integral. This non-linear transformation incurs a severe loss of contextual information that is mathematically unaccounted for in Bell’s original derivation. By failing to recognize this measure-theoretic mismatch the subsequent deductions, including the assertion that a remote measurement setting must dynamically influence a distant apparatus, are rendered logically invalid. Consequently, the attribution of non-locality to Einstein-Podolsky-Rosen-Bohm (EPRB) systems is shown to be an unfounded artifact of this misapplied probability space rather than an empirical property of physical nature.