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Conditional expectations, conditional distributions, and a posteriori ensembles in generalized probability theory. (English) Zbl 0645.60007
Summary: A general probabilistic framework containing the essential mathematical structure of any statistical physical theory is reviewed and enlarged to enable the generalization of some concepts of classical probability theory. In particular, generalized conditional probabilities of effects and conditional distributions of observables are introduced and their interpretation is discussed in terms of successive measurements.
The existence of generalized conditional distributions is proved, and the relation to M. Ozawa’s [Publ. Res. Inst. Math. Sci. 21, 279-295 (1985; Zbl 0576.60005)] a posteriori states is investigated. Examples concerning classical as well as quantum probability are discussed.

60A99 Foundations of probability theory
82B99 Equilibrium statistical mechanics
Full Text: DOI
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