Statistical maps. II: Operational random variables and the Bell phenomenon

 Access to full text

 Full (PDF)

1. BELL J. S., On the Einstein-Podolsky-Rosen paradox, Physics 1 (1964), 195-200. (1964) 
2. FINE A., Hidden variables, joint probability, and the Bell inequalities, Phys. Rev. Lett. 48 (1982), 291-295. (1982) MR0642943
3. FINE A., Joint distributions, quantum correlations, and commuting observables, J. Math. Phys. 23 (1982), 1306-1310. (1982) MR0666180
4. BELTRAMETTI E. G.-BUGAJSKI S., The Bell phenomenon in classical frameworks, J. Phys. A 29 (1996), 247-261. (1996) Zbl0914.46060MR1381557
5. ACCARDI L.-CECCHINI, C, Conditional expectations on von Neumann algebras and a theorem of Takesaki, J. Funct. Anal. 45 (1982), 245-273. (1982) MR0647075
6. ACCARDI L.-FRIGERIO A.-LEWIS J. T., Quantum stochastic processes, Publ. Res. Inst. Math. Sci. 18 (1982), 97-133. (1982) Zbl0498.60099MR0660823
7. STREATER R. F., Classical and quantum probability, arXiv:math-ph/0002029 (27 Feb 2000). Zbl0981.81006MR1768632
8. BUSCH P.- GRABOWSKI M.-LAHTI P. J., Operational Quantum Physics, Springer-Verlag, Berlin, 1995. (1995) MR1356220
9. BUGAJSKI S., Fundamentals of fuzzy probability theory, Internat. J. Theoret. Phys. 35 (1996), 2229-2244. (1996) Zbl0872.60003MR1423402
10. BUGAJSKI S.-HELLWIG K.-E.-STULPE W., On fuzzy random variables and statistical maps, Rep. Math. Phys. 41 (1998), 1-11. (1998) Zbl1026.60501MR1617902
11. BUGAJSKI S., Fuzzy stochastic processes, Open Syst. Inf. Dyn. 5 (1998), 169-185. (1998) Zbl0908.60044
12. GUDDER S., Fuzzy probability theory, Demonstratio Math. 31 (1998), 235-254. (1998) Zbl0984.60001MR1623780
13. BUGAJSKI S., Statistical maps I. Basic properties, Math. Slovaca 51 (2001), 321 342. Zbl1088.81021MR1842320
14. BUGAJSKI S., Classical and quantal in one or How to describe mesoscopic systems, Molecular Phys. Rep. 11 (1995), 161-171. (1995) 
15. PURI M. L.-RALESCU D. A., Fuzzy random variables, J. Math. Anal. Appl. 114 (1986), 409-422. (1986) Zbl0605.60038MR0833596
16. RIEČAN B.-NEUBRUNN T., Integral, Measure, and Ordering, Math. Appl. 411, Kluwer, Dordrecht, 1997. (1997) Zbl0916.28001MR1489521
17. BAUER H., Probability Theory and Elements of Measure Theory, Academic Press, London, 1981. (1981) Zbl0466.60001MR0636091
18. HOLEVO A. S., Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam, 1982. (1982) Zbl0497.46053MR0681693
19. BUSCH P.-LAHTI P. J.-MITTELSTAEDT P., The Quantum Theory of Measurement, (2nd ed.), Springer-Verlag, Berlin, 1996. (1996) Zbl0868.46051MR1419313
20. ARAKI H., A remark on Machida-Namiki theory of measurement, Progr. Theoret. Phys. 64 (1980), 719-730. (1980) Zbl1097.81503MR0596946
21. VON NEUMANN J., Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, N.J., 1955. (1955) Zbl0064.21503MR0066944
22. MISRA B., On a new definition of quantal states, In: Physical Reality and Mathematical Description (C P. Enz, J. Mehra, eds.), D. Reidel Publishing Company, Dordrecht-Holland, 1974, pp. 455-476. (1974) 
23. BELTRAMETTI E. G.-BUGAJSKI S., Quantum observables in classical frameworks, Internat. J. Theoret. Phys. 34 (1995), 1221-1229. (1995) Zbl0850.81019MR1353665
24. BELTRAMETTI E. G.-BUGAJSKI S., A classical extension of quantum mechanics, J. Phys. A 28 (1995), 3329-3343. (1995) Zbl0859.46049MR1344371
25. BOHM D., Quantum Theory, Prentice-Hall, Inc, Englewood Cliffs, NJ., 1951. (1951) 

1. Sławomir Bugajski, Statistical maps. I: Basic properties
2. Roman Frič, Martin Papčo, Fuzzification of crisp domains
3. Roman Frič, Statistical maps: a categorical approach
4. Roman Frič, Martin Papčo, Upgrading Probability via Fractions of Events
5. Roman Frič, Duality for generalized events