| Title:
|
A measure-theoretic characterization of Boolean algebras among orthomodular lattices (English) |
| Author:
|
Pták, Pavel |
| Author:
|
Pulmannová, Sylvia |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
205-208 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures. This result may find an application in the foundation of quantum theories, mathematical logic, or elsewhere. (English) |
| Keyword:
|
orthomodular lattice |
| Keyword:
|
subadditive probability measure |
| MSC:
|
03G12 |
| MSC:
|
06C15 |
| MSC:
|
28E15 |
| MSC:
|
81P10 |
| idZBL:
|
Zbl 0805.06010 |
| idMR:
|
MR1292596 |
| . |
| Date available:
|
2009-01-08T18:10:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118654 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Foulis D.J.: A note on orthomodular lattices.Portugal. Math. 21 (1962), 65-72. Zbl 0106.24302, MR 0148581 |
| Reference:
|
[4] Greechie R.J.: Orthomodular lattices admitting no states.Jour. Comb. Theory 10 (1971), 119-132. Zbl 0219.06007, MR 0274355 |
| Reference:
|
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| Reference:
|
[6] Kalmbach G.: Orthomodular Lattices.Academic Press, London, 1983. Zbl 0554.06009, MR 0716496 |
| Reference:
|
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| Reference:
|
[8] Müller V.: Jauch-Piron states on concrete quantum logics.Int. Jour. Theor. Phys. 32 (1993), 433-442. MR 1213098 |
| Reference:
|
[9] Pták P.: Exotic logics.Colloquium Math., Vol. LIV (1987), 1-7. MR 0928651 |
| Reference:
|
[10] Pták P., Pulmannová S.: Orthomodular Structures as Quantum Logics.Kluwer Academic Publishers, Dordrecht-Boston-London, 1991. MR 1176314 |
| Reference:
|
[11] Riečanová Z.: Topology in a quantum logic induced by a measure.Proc. Conf. Topology and Measure V, Greifswald (1988), 126-130. MR 1029570 |
| Reference:
|
[12] Rüttimann G., Wright J.D.M.: Kalmbach outer measures and evaluations.to appear. |
| Reference:
|
[13] Sarymsakov T., Ajupov S., Khadzhiev D., Chilin V.: Ordered Algebras (in Russian).Filial AN, Tashkent, 1983. |
| . |
