Skip to main content
Log in

On the Joint Distribution of Observables

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

A general algebraic system M is considered with two binary operations. The family of all measurable functions with values in the unit interval is a motivating example. A state is a morphism from M to the unit interval, an observable is a morphism from the family of Borel sets to M. A joint distribution of two observables is constructed. It is applied for the construction of the sum of observables and for a representation of conditional probability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. A.Dvurecenskij and B.Riecan, “Weekly divisible MV algebras and product,” J.Math.Anal.Appl., to appear.

  2. A.Kacian, “Construction of joint observable for l-ring valued measures,” Busefal 75, 97-100.

  3. A. Kacian and B. Riecan, “Sum of weak observables in MV algebras,” IPMU 1998 2, 1398–1402 (1998).

    Google Scholar 

  4. D. Mundici, “Interpretation of AFC*-algebras in 4ukasiewicz sentential calculus,” J.Funct.Anal. 65, 15–63 (1986).

    Google Scholar 

  5. B. Riecan, “Probability theory on some ordered structures,” Atti Sem.Mat.Fis.Univ.Modena 47, 255–265 (1999).

    Google Scholar 

  6. B. Riecan, “On the product MV algebras,” Tatra Mt.Math.Publ. 16, 143–150 (1999).

    Google Scholar 

  7. B.Riecan, “Weak observables in MV algebras,” Int.J.Theor.Phys., to appear.

  8. B. Riecan, “On the conditional probability on MV algebras,” Prague Stochastic 1998, 486–486 (1998).

  9. B. Riecan and T. Neubrunn, Integral, Measure, and Ordering (Kluwer Academic, Dordrecht, 1997; Science, Bratislava, 1997).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Riečan, B. On the Joint Distribution of Observables. Foundations of Physics 30, 1679–1686 (2000). https://doi.org/10.1023/A:1026402301407

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026402301407

Keywords

Navigation