Nonsignaling as the consistency condition for local quasi classical probability modelling of a general multipartite correlation scenario

We specify for a general correlation scenario a particular type of a local quasi hidden variable (LqHV) model [J. Math. Phys. 53 (2012), 022201] -- a deterministic LqHV model, where all joint probability distributions of a correlation scenario are simulated via a single measure space with a normalized bounded real-valued measure not necessarily positive and random variables, each depending only on a setting of the corresponding measurement at the corresponding site. We prove that an arbitrary multipartite correlation scenario admits a deterministic LqHV model if and only if all its joint probability distributions satisfy the consistency condition constituting the general nonsignaling condition formulated in [J. Phys. A: Math. Theor. 41 (2008), 445303]. This mathematical result specifies a new probability model that has the measure-theoretic structure resembling the structure of the classical probability model but incorporates the latter only as a particular case. The local version of this quasi classical probability model covers the probabilistic description of every nonsignaling correlation scenario, in particular, each correlation scenario on an multipartite quantum state.