Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-12T17:06:40.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Conditioning maps on orthomodular lattices

Published online by Cambridge University Press:  18 May 2009

D. J. Foulis and
C. H. Randall
D. J. Foulis
Affiliation:
The University of Massachusetts, Amherst, Massachusetts
C. H. Randall
Affiliation:
The University of Massachusetts, Amherst, Massachusetts
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Let (χ Σ, μ) be a probability space, so that X is a non-empty set, Σ is a Boolean a-algebra of subsets of X, and μ is a probability measure defined on Σ. If D Ε S is such that μ(D)≠0, then one traditionally associates with D a new probability measure μD, called the conditional probability measure determined by D, and defined by μD(E)= μ(D∩E)/μ(D), for all EΕΣ.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 12 , Issue 1 , April 1971, pp. 35 - 42
Copyright
Copyright © Glasgow Mathematical Journal Trust 1971

References

REFERENCES

1.Birkhoff, G., Lattice Theory, Amer. Math. Soc. Colloquium Pub. XXV (Providence, R. I., 1967).Google Scholar
2.Dacey, J. C. Jr, Orthomodular Spaces, Ph. D. Thesis, Univ. of Mass., Amherst, Mass., 1968.Google Scholar
3.Derderian, J. C., Residuated mappings, Pacific J. Math. 20 (1967), 35–43.CrossRefGoogle Scholar
4.Foulis, D. J., A note on orthomodular lattices, Portugaliae Math. 21, Fasc. 1 (1962), 65–72.Google Scholar
5.Foulis, D. J. and Randall, C. H., Lexicographic orthogonality (to appear in J. Combinatorial Theory).Google Scholar
6.Pool, J. C. T., Baer *-semigroups and the logic of quantum mechanics, Commitn. Math. Phys. 9 (1968), 118–141.CrossRefGoogle Scholar
7.Randall, C. H., A Mathematical Foundation for Empirical Science with Special Reference to Quantum Theory, Knolls Atomic Power Lab. Report KAPL-3147 (1966).Google Scholar
8.Randall, C. H. and Foulis, D. J., An approach to empirical logic, Amer. Math. Monthly 11 (1970), 363–374.CrossRefGoogle Scholar