Title: Foundations of non-commutative probability theory

Abstract: Kolmogorov's setting for probability theory is given an
original generalization to account for probabilities arising from
Quantum Mechanics. The sample space has a central role in this
presentation and random variables, i.e., observables, are defined in a
natural way. The mystery presented by the algebraic equations
satisfied by (non-commuting) observables that cannot be observed in
the same states is elucidated.