ON INTERSECTION OF PROBLEMS OF THEORETICAL STATISTICS AND SET THEORY

Gogi Pantsulaia (Georgia)

Received December 20, 2007

References:

[1] J. Cichon, A. Kharazishvili and B. Weglorz, Subsets of the Real Line, Wydaw-Nictwo Uniwersytetu Lodzkiego, Lodz, 1995. [2] P. J. Cohen, Set Theory and the Continuum Hypothesis, Benjamin, New York, 1966. [3] P. R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950. [4] B. R. Hurt, T. Sauer and J. A. Yorke, Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces, Bull. Amer. Math. Soc. 27(2) (1992), 217-238. [5] I. Sh. Ibramkhallilov and A. V. Skorokhod, On Well-off Estimates of Parameters of Stochastic Processes, Kiev, 1980 (in Russian). [6] I. Jech, Lectures in Set Theory, Springer, Berlin, 1973. [7] A. B. Kharazishvili, Topological Aspects of Measure Theory, Naukova Dumka, Kiev, 1984 (in Russian). [8] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), 143-178. [9] G. R. Pantsulaia, Some properties of families of probability measures, Soobshch. Akad. Nauk Gruzin. SSR 120(2) (1985), 245-248 (in Russian). [10] G. R. Pantsulaia, On orthogonal families of probability measures, Trans. GPI 8(350) (1989), 106-112 (in Russian). [11] G. R. Pantsulaia, On separation properties for families of probability measures, Georgian Math. J. 10(2) (2003), 335-342. [12] A. V. Skorokhod, Integration in Hilbert Space, Nauka, Moscow, 1975; English transl.: Springer, 1974. [13] R. M. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Ann. Math. 92 (1970), 1-56. [14] N. N. Vakhanya, V. I. Tarieladze and S. A. Chobanyan, Probability Distributions in Banach Spaces, Nauka, Moscow, 1985 (in Russian). [15] Z. S. Zerakidze, On weakly separated and separated families of probability measures, Bull. Acad. Sc. Georgian SSR 113(2) (1984), 273-275 (in Russian). [16] Z. S. Zerakidze, The composition of statistical structures, Teor. Veroyatnost. i Primenen. 31(3) (1986), 573-577 (in Russian).

Keywords and phrases: Martin’s axiom, continuum hypothesis, radon space, separated family of probability measures.