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Given a physical quantum system described by a Hilbert H, for any boundedquantum observable (a bounded self-adjoint operator) T it is possible to defineseveral ''hidden observable'' functions f:H->R associated to T and for anyquantum mixed state (a density matrix) D it is possible to define several''hidden mixed states'' (probability measures) m on H associated to D in such away that the following equality is verified:  Trace[ b(T). D] =integral[b(f(psi)).dm(psi) whatever is the continuousfunction b:R->R. This formula gives a general way to express any expectationvalue computable in a quantum theory as a classical statistical mean value.

All quantum expectation values as classical statistical mean values