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In this chapter we recall some definitions of quantum probability theory in the general framework developed by Accardi and several co-workers. Several expository papers in the series Quantum Probability and Related Topics and two monographes 68, 74 are already available in the literature. We will only illustrate the definitions by two examples which are included only with the aim to give a flavour of the relation with classical probability.
Franco Fagnola (Wed,) studied this question.