Geodesic
Set functions and probability distributions of a finite random sets
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 362-371.

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This paper is the investigation of the probability distributions of a finite random set in which the set of random events are considered as a support of the finite random set. These probability distributions can be defined by six equivalent ways (distributions of the I-st–VI-th type). Each of these types of the probability distributions is the set function defined on the corresponding system of events. In this paper the sufficient conditions are formulated and proved. When these conditions are satisfied, then the set function determines the probability distributions of the finite random set of the II-nd and the V-th type. The found conditions supplement the known necessary conditions for the existence of the probability distributions of a finite random set of the II-nd and the V-th type.
Keywords: finite random set, set function, probability distribution. 
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Natalia A. Lukyanova; Daria V. Semenova; Elena E. Goldenok. Set functions and probability distributions of a finite random sets. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 362-371. http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a14/

[1] I. Molchanov, The Theory of Random Sets, Springer, New York, 2011 | MR

[2] H.T. Nguyen, An Introduction to Random Sets, Taylor Francis Group, LLC, 2006 | MR

[3] O. Yu. Vorobyev, Eventology, Siberian Federal University, Krasnoyarsk, 2007 (in Russian)

[4] A. I. Orlov, Stability in the socio-economic models, Nauka, M., 1979 (in Russian) | MR

[5] N. A. Lukyanova, D. V. Semenova, “Associative Frank functions in constructing families of discrete probability distributions of random sets of events”, Zh. prikladnoi diskretnoi matematiki, 32:2 (2016), 5–19 (in Russian) | DOI | MR

[6] D. V. Semenova, N. A. Lukyanova, Recurrent formation of discrete probabilistic distributions of random sets of events, 26:4 (2014), 47–58 (in Russian)

[7] N. A. Lukyanova, D. V. Semenova, J. of Siberian Federal University. Math. Phys., 7:4 (2014), The study of discrete probabilistic distributions of random sets of events using associative function

[8] D. V. Semenova, N. A. Lukyanova, “Formation of Probabilistic Distributions of RSE by Associative Functions”, Communications in Computer and Information Science, 487, Springer International Publishing, Switzerland, 2014, 377–386 | DOI | Zbl

[9] O. Yu. Vorobyev, A. O. Vorobyev, “Summation of the set-additive functions and Mobius inversion formula”, Doklady Ross. Akad. Nauk, 336:4 (1994), 417–420 (in Russian) | MR

[10] A. N. Shiryaev, Probability, v. 1, M., 2004 (in Russian) | MR