Per K. Jakobsen and Valentin V. Lychagin

Operator valued probability theory

(Lobachevskii Journal of Mathematics, Vol.16, pp.17 - 56)

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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