Conditional probabilities on orthomodular lattices. (English) Zbl 0564.60003
A definition of generalized probability on an orthomodular lattice which includes as particular cases the classical probability space and non- commutative probability theory on a von Neumann algebra is proposed. In this generalized structure the problem of conditioning with respect to Boolean \(\sigma\)-subalgebras is examined.
MSC:
| 60A10 | Probabilistic measure theory |
| 46L51 | Noncommutative measure and integration |
| 46L53 | Noncommutative probability and statistics |
| 46L54 | Free probability and free operator algebras |
| 06C15 | Complemented lattices, orthocomplemented lattices and posets |
Keywords:
probability on an orthomodular lattice; non-commutative probability theory; von Neumann algebraReferences:
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