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Minimization of a convex functional on a class of sets in a measure space

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Literature cited

  1. P. Levy, Concrete Problems of Functional Analysis [Russian translation], Nauka, Moscow (1967).

    Google Scholar 

  2. H. Sergin, “A variational problem arising in economics: approximate solutions and the law of large numbers,” in: Game Theory and Mathematical Economics, North-Holland, New York (1981).

    Google Scholar 

  3. M. Mangel, “Optimal search for and mining of underwater mineral resources,” SIAM J. Appl. Math.,43, No. 1, 99–106 (1983).

    Google Scholar 

  4. A. L. Garkavi, “Approximative centers and nets of sets in a normed linear space. Approximation theory of functions,” in: Proceedings of the International Conference on Approximation Theory [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  5. A. L. Garkavi and V. A. Kaminskii, “Minimization of functionals on measure spaces and the confidence center of the set,” Revue Roumaine de Mathematiques pures et appliquees,”25, No. 8, 1207–1223 (1980).

    Google Scholar 

  6. G. P. Tolstov, Measure and Integral [in Russian], Nauka, Moscow (1976).

    Google Scholar 

  7. A. A. Lyapunov, “On completely integrable vector-functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,4, 465–478 (1940).

    Google Scholar 

  8. G. G. Roussas, Continuity of Probability Measures, Cambridge Univ. Press, New York (1972).

    Google Scholar 

  9. N. Dunford and J. T. Schwartz, Linear Operators. General Theory, Interscience, New York (1958).

    Google Scholar 

  10. V. I. Averbukh, O. G. Smolyanko, and S. V. Fomin, “Generalized functions and differential equations on linear paces. I. Differential measures,” Tr. Mosk. Mat. Ob.,24, 133–174 (1971).

    Google Scholar 

  11. I. Ekeland R. Temam, Convex Analysis and Variational Problems, North-Holland, New York (1976).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 47, No. 1, pp. 81–91, January, 1990.

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Kaminskii, V.A. Minimization of a convex functional on a class of sets in a measure space. Mathematical Notes of the Academy of Sciences of the USSR 47, 53–59 (1990). https://doi.org/10.1007/BF01157284

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  • DOI: https://doi.org/10.1007/BF01157284

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