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Title

Some problems in measure theory

Authors 1

Affiliations

  1. Institute of Applied Mathematics, University of Tbilisi, University St. 2, 380043 Tbilisi 43, Georgia, U.S.S.R.

Bibliography

  1. J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam 1977.
  2. P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
  3. N. Bourbaki, Topologie générale, Hermann, Paris 1958.
  4. N. Bourbaki, Intégration, Hermann, Paris 1963.
  5. V. V. Buldygin and A. B. Kharazishvili, Borel measures in nonseparable metric spaces, Ukrain. Mat. Zh. 29 (5) (1983), 552-556 (in Russian); English transl.: Ukrainian Math. J. 35 (1983), 465-470.
  6. V. V. Buldygin and A. B. Kharazishvili, Cylindrical and Borel σ-algebras, Ukrain. Mat. Zh. 38 (1) (1986), 12-17; English transl.: Ukrainian Math. J. 38 (1986), 12-17.
  7. C. Dellacherie, Capacités et processus stochastiques, Springer, Berlin 1972.
  8. M. P. Ershov, Extensions of measures, and stochastic equations, Teor. Veroyatnost. i Primenen. 19 (1974), 457-451; English transl.: Theor. Probab. Appl. 19 (1974), 431-444.
  9. D. H. Fremlin, Borel sets in nonseparable Banach spaces, Hokkaido Math. J. 9 (2) (1980), 179-183.
  10. R. J. Gardner and W. F. Pfeffer, Borel Measures, in: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam 1984, 961-1043.
  11. P. R. Halmos, Measure Theory, D. Van Nostrand, New York 1950.
  12. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Springer, Berlin 1963.
  13. I. Sh. Ibramkhalilov and A. B. Skorokhod, Consistent Estimators of Parameters of Random Processes, Naukova Dumka, Kiev 1980 (in Russian).
  14. J. L. Kelley, Measures in Boolean algebras, Pacific J. Math. 9 (1959), 1165-1177.
  15. A. B. Kharazishvili, The Szpilrajn-Marczewski axiom for extensions of the Lebesgue measure, Soobshch. Akad. Nauk Gruzin. SSR 96(1)(1979), 17-20 (in Russian).
  16. A. B. Kharazishvili, Some Problems of Functional Analysis and Their Applications, Tbiliss. Gos. Univ., Tbilisi 1979 (in Russian).
  17. A. B. Kharazishvili, Quasi-invariant measures in topological groups, Soobshch. Akad. Nauk Gruzin. SSR 108 (2) (1982), 277-288 (in Russian).
  18. A. B. Kharazishvili, Invariant measures in Hilbert space, ibid. 114 (1) (1984), 41-48 (in Russian).
  19. A. B. Kharazishvili, On the existence of quasi-invariant measures, ibid. 115 (1) (1984), 37-40 (in Russian).
  20. A. B. Kharazishvili, Topological Aspects of Measure Theory, Naukova Dumka, Kiev 1984 (in Russian).
  21. A. B. Kharazishvili, Perfect probability spaces, Soobshch. Akad. Nauk Gruzin. SSR 131 (1) (1988), 37-40 (in Russian).
  22. A. B. Kharazishvili, On the existence of estimates for strongly separable families of probability measures, Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 92 (1989), 100-105 (in Russian).
  23. A. Kolmogoroff, La définition axiomatique de l'intégrale, C. R. Acad. Sci. Paris 180 (1925), 110-111.
  24. K. Kuratowski, Topology, Vol. 1, Academic Press, New York 1966.
  25. J. Neveu, Bases mathématiques du calcul des probabilités, Masson, Paris 1964.
  26. J. C. Oxtoby, Measure and Category, Springer, New York 1980.
  27. D. Preiss, Metric spaces in which Prohorov's theorem is not valid, Z. Wahrsch. Verw. Gebiete 27 (2) (1973), 109-116.
  28. L. Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford University Press, London 1973.
  29. S. Shelah, Can you take Solovay's inaccessible away?, Israel J. Math. 48 (1) (1984), 1-47.
  30. J. R. Shoenfield, Mathematical Logic, Addison-Wesley, Reading, Mass., 1967.
  31. R. Sikorski, Boolean Algebras, Springer, New York 1969.
  32. A. V. Skorokhod, Integration in Hilbert Space, Nauka, Moscow 1975; English transl.: Springer, 1974.
  33. E. Szpilrajn (E. Marczewski), On the problems of measure theory, Uspekhi Mat. Nauk 1 (2) (12) (1946), 179-188; English transl. in preparation.
  34. N. N. Vakhaniya, V. I. Tarieladze and S. A. Chobanyan, Probability Distributions in Banach Spaces, Nauka, Moscow 1985 (in Russian).
  35. M. L. Wage, The product of Radon spaces, Uspekhi Mat. Nauk 35 (3) (1980), 151-153 (in Russian); English transl.: Russian Math. Surveys 35 (1980), 185-187.
Colloquium Mathematicum
1991/62/2
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Pages:
197-220
Main language of publication
English
Received
1988-09-22
Accepted
1990-10-19
Published
1991
Exact and natural sciences