Matúš, František Discrete marginal problem for complex measures. (English) Zbl 0636.60002 Kybernetika 24, No. 1, 36-46 (1988). This paper contains complete analysis of the problem to find all complex measures (on the Cartesian product of a finite system of finite nonempty sets) for which the family of its marginal measures is identical with a given family of complex measures. The transformation, mapping every density of the complex measure into the family of its marginal densities, called here the discrete Radon transform, is considered together with its dual transform and their inversions are given in effective forms. Illustrating examples are added. Cited in 1 Document MSC: 60A99 Foundations of probability theory 28A99 Classical measure theory Keywords:complex measures; marginal measures; discrete Radon transform; dual transform; inversions PDF BibTeX XML Cite \textit{F. Matúš}, Kybernetika 24, No. 1, 36--46 (1988; Zbl 0636.60002) Full Text: EuDML Link OpenURL References: [1] H. G. Kellerer: Masstheoretische Marginalprobleme. Math. Ann. 153 (1964), 168-198. · Zbl 0118.05003 [2] H. G. Kellerer: Verteilungsfunktionen mit gegebenem Marginalverteilungen. Z. Wahrsch. verw. Gebiete 3 (1964), 247-270. · Zbl 0126.34003 [3] M. Studený: On Existence of Probability Measures with Given Marginals. Research Report, ÚTIA ČSAV, Praha 1986. [4] M. Studený: The notion of multiinformation in probabilistic decision. Ph. D. Dissertation, ÚTIA ČSAV, Praha 1987. [5] A. Perez, R. Jiroušek: Constructing an intensional expert system (INES). Medical Decision Making: diagnostic strategies and expert systems, North Holland, Amsterdam–New York–Oxford 1985, pp. 307-315. [6] S. Helgason: The Radon Transform. Birkäuser, Boston–Basel–Stuttgart 1980. · Zbl 0453.43011 [7] G. T. Herman: Image Reconstruction from Projections. Springer-Verlag, Berlin–Heidelberg–New York 1980. · Zbl 0538.92005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.