Abstract
The paper deals with an area that studies measures that are uniquely determined by their restriction to a sufficiently abundant set. This area began to develop in the 1970s under the initiative of V. M. Zolotarev. Its present state is reflected in [1, 2], where a detailed bibliography can be found.
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References
H.-J. Rossberg, B. Jesiak, and G. Siegel, Analytic Methods of Probability Theory, Akademie-Verlag, Berlin (1985).
I. V. Ostrovskii and A. M. Ulanovskii, "Classes of complex-valued Borel measures with unique determination by restrictions," Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,170, 233–253 (1989).
I. A. Ibragimov, "On the determination of an infinitely divisible distribution function from its values on a semiline," Teor. Veroyatn. Primenen.,22, No. 2, 393–399 (1977).
I. V. Ostrovskii, "Generalization of the Titchmarsh convolution theorem and the complex-valued measures uniquely determined by their restrictions to a half-line," Lecture Notes in Math., No. 1155, Springer, Berlin (1985), pp. 256–283.
A. M. Ulanovskii, "On the unique determination of convolutions of measures inR m, m ≥ 2, by restrictions to sets," Teor. Funkts. Funktsional. Anal. Prilozhen. (Khar'kov), No. 50, 86–90 (1988).
A. I. Il'inskii, "Some remarks on the uniqueness of the extension of measures from subsets to the group Z2 ×R," in: Stability Problems for Stochastic Models (Proc. Internat. Seminar held in Sukhumi, October 1987), Vses. Nauch.-Issled. Inst. Sistem. Issled., Moscow (1988), pp. 55–59.
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Springer, Berlin (1963).
O. B. Skaskiv, "A generalization of the little Picard theorem," Teor. Funkts. Funktsional. Anal. Prilozhen. (Khar'kov), No. 46, 90–100 (1986).
A. M. Ulanovskii, "Determination of the n-fold convolution of a distribution function from its values on a system of intervals," Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 3, 32–35 (1988).
Yu. V. Linnik (Ju. V. Linnik) and I. V. Ostrovskii, Decomposition of Random Variables and Vectors, Amer. Math. Soc., Providence (1977).
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 2, Springer, Berlin (1970).
A. A. Gol'dberg, "Some questions of value distribution theory." Appendix to the Russian translation of H. Wittich, Neuere Untersuchungen über eindeutige analytische Funktionen, Fizmatgiz, Moscow (1960), pp. 263–300.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 184, pp. 264–270, 1990.
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Ulanovskii, A.M. Measures on locally compact abelian groups, whose n-fold convolutions are determined by the restrictions to a massive set. J Math Sci 68, 588–591 (1994). https://doi.org/10.1007/BF01254286
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DOI: https://doi.org/10.1007/BF01254286