Statistical maps. I: Basic properties

Sławomir Bugajski

Mathematica Slovaca (2001)

  • Volume: 51, Issue: 3, page 321-342
  • ISSN: 0139-9918

How to cite

top

Bugajski, Sławomir. "Statistical maps. I: Basic properties." Mathematica Slovaca 51.3 (2001): 321-342. <http://eudml.org/doc/32070>.

@article{Bugajski2001,
author = {Bugajski, Sławomir},
journal = {Mathematica Slovaca},
keywords = {statistical map; Markov kernel; effect valued measure; operational probability theory},
language = {eng},
number = {3},
pages = {321-342},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Statistical maps. I: Basic properties},
url = {http://eudml.org/doc/32070},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Bugajski, Sławomir
TI - Statistical maps. I: Basic properties
JO - Mathematica Slovaca
PY - 2001
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 51
IS - 3
SP - 321
EP - 342
LA - eng
KW - statistical map; Markov kernel; effect valued measure; operational probability theory
UR - http://eudml.org/doc/32070
ER -

References

top
  1. ALFSEN E. M., Compact Convex Sets and Boundary Integrals, Springer, Berlin, 1971. (1971) Zbl0209.42601MR0445271
  2. ASIMOW L.-ELLIS A. J., Convexity Theory and Its Applications in Functional Analysis, Academic Press, London, 1980. (1980) Zbl0453.46013MR0623459
  3. BARRA J. R., Notions fondamentales de statistique mathématique, Dunod, Paris, 1971. (1971) Zbl0257.62004MR0402992
  4. BAUER H., Probability Theory and Elements of Measure Theory, Academic Press, London, 1981. (1981) Zbl0466.60001MR0636091
  5. BELTRAMETTI E. G.-BUGAJSKI S., A Classical extension of quantum mechanics, J. Phys. A 28 (1995), 3329-3343. Quantum observables in classical frameworks, Internat. J. Theoгet. Phys. 34 (1995), 1221-1229. (1995) Zbl0859.46049MR1344371
  6. BELTRAMETTI E. G.-BUGAJSKI S., Effect algebras and statistical physical theories, J. Math. Phys. 38 (1997), 3020-3030. (1997) Zbl0874.06009MR1449546
  7. BILLINGSLEY P., Ergodic Theory and Information, Wiley, New York, 1965. (1965) Zbl0141.16702MR0192027
  8. BILLINGSLEY P., Probability and Measure, Wiley, New Yoгk, 1979. (1979) Zbl0411.60001MR0534323
  9. BUGAJSKI S., Fundamentals of fuzzy probability theory, Internat. J. Theoret. Phys. 35 (1996), 2229-2244. (1996) Zbl0872.60003MR1423402
  10. BUGAJSKI S., Fuzzy stochastic processes, Open Syst. Inf. Dyn. 5 (1998), 169-185. (1998) Zbl0908.60044
  11. BUGAJSKI S., Net entropies of fuzzy stochastic processes, Open Syst. Inf. Dyn. 5 (1998), 187-200. (1998) Zbl0908.60044
  12. BUGAJSKI S., Fuzzy dynamics in terms of fuzzy probability theory, In: IFSA '97 Prague. Seventh International Fuzzy Systems Association World Congress. Proceedings Vol. IV (M. Mareš, R. Mesiar, V. Novák, J. Ramík, A. Stupňanová, eds.), Academia, Pгague, 1997, pp. 255-260. (1997) 
  13. BUGAJSKI S., Statistical maps II. Operational random variables and the Bell phenomenon, Math. Slovaca 51 (2001), 343-361. Zbl1088.81022MR1842321
  14. BUGAJSKI S.-HELLWIG K.-E.-STULPE W., On fuzzy random variables and statistical maps, Rep. Math. Phys. 41 (1998), 1-11. (1998) Zbl1026.60501MR1617902
  15. BUSCH P.-RUCH E., The measure cone: irreversibüity as a geometrical phenomenon, Internat. J. Q. Chem. 41 (1992), 163-185. (1992) 
  16. GUDDER S., Fuzzy probability theory, Demonstratio Math. 31 (1998), 235-254. (1998) Zbl0984.60001MR1623780
  17. MACKEY G., The Mathematical Foundations of Quantum Mechanics., Benjamin, New York, 1963. (1963) Zbl0114.44002
  18. NEVEU J., Mathematical Foundations of the Calculus of Probability, Holden-Day, Inc, San Francisco, 1965 [French original: Bases mathématiques du calcul des probabilités, Mason et Cie, Paris, 1964]. (1965) Zbl0137.11301MR0198505
  19. REED M.-SIMON B., Methods of Modern Mathematical Physics 1, Functional Analysis, Academic Press, New York, 1972. (1972) Zbl0242.46001
  20. RIEČAN B.-NEUBRUNN T., Integral, Measure, and Ordeńng, Math. Appl. 411, Kluwer, Dordrecht, 1997. (1997) 
  21. RUDIN W., Functional Analysis, McGraw-Hill, New York, 1973. (1973) Zbl0253.46001MR0365062
  22. SCHAEFER H. H., Topological Vector Spaces, (Зrd ed.), Springer-Verlag, Berlin, 1971. (1971) Zbl0217.16002MR0342978
  23. SINGER M.-STULPE W., Phase-space representations of general statistical physical theories, J. Math. Phys. 33 (1992), 131-142. (1992) MR1141510
  24. STULPE W., Conditional expectations, conditional distributions, and a posteriori ensembles in generalized probability theory, Internat. J. Theoret. Phys. 27 (1988), 587-611. (1988) Zbl0645.60007MR0950546
  25. VERSIK A. M., Multivalued mappings with invariant measure (polymorphisms) and Markov operators, Zap. Nauchn. Sem. S.-Peterburg. (Leningrad.) Otdel. Mat. Inst. Steklov. (POMI) ((LOMI)) 72 (1977), 26-61, 223. (Russian) (1977) MR0476998
  26. WERNER R., Physical uniformities on the state space of nonrelativistic quantum mechanics, Found. Phys. 13 (1983), 859-881 MR0788064

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.