Conditional expectations,conditional distributions,anda posteriori ensembles in generalized probability theory

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'sa posteriori states is investigated. Examples concerning classical as well as quantum probability are discussed.