Geodesic
Operator valued probability theory
Lobachevskii journal of mathematics, Tome 16 (2004), pp. 17-56.

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We outline an extention of probability theory based on positive operator valued measures. We generalize the main notions from probability theory such as random variables, conditional expectations, densities and mappings. We introduce a product of extended probability spaces and mappings, and show that the resulting structure is a monoidal category, just as in the classical theory. 
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P. K. Jakobsen; V. V. Lychagin. Operator valued probability theory. Lobachevskii journal of mathematics, Tome 16 (2004), pp. 17-56. http://geodesic.mathdoc.fr/item/LJM_2004_16_a1/

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