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Narrow convergence in spaces of set-valued measures

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Języki publikacji
EN
Abstrakty
EN
We prove an analogue of Topsøe's criterion for relative compactness of a family of probability measures which are regular with respect to a family sets. We consider measures whose values are compact convex sets in a locally convex linear topological space.
Rocznik
Strony
15--24
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
  • Department of Mathematics, Faculty of Sciences, University of Lome, P.O. Box 1515, Lome, Togo, ksiggini@hotmail.com
Bibliografia
  • [1] N. Bourbaki, Intégration, chapitre IX, Hermann, Paris.
  • [2] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, 1977.
  • [3] J. B. Conway, The strict topology and compactness in the space of measures, Trans. Amer. Math. Soc. 126 (1967), 474-486.
  • [4] N. Dunford and J. T. Schwartz, Linear Operators, Part I, General Theory, Interscience, New York, 1958.
  • [5] X. Fernique, Processus linéaires, processus généralisés, Ann. Inst. Fourier (Grenoble) 17 (1967), no. 1, 1-92.
  • [6] D. H. Fremlin, D. J. H. Garling and R. G. Haydon, Bounded measures on topological spaces, Proc. London Math. Soc. (3) 25 (1972), 115-136.
  • [7] G. Köthe, Topological Vector Spaces I, 2nd ed., Springer, Berlin, 1983.
  • [8] L. Le Cam, Convergence in distribution of stochastic processes, Univ. Calif. Publ. Statist. 2 (1957), 207-236.
  • [9] S. E. Mosiman and R. F. Wheeler, The strict topology in a completely regular setting: Relations to topological measure theory, Canad. J. Math. 24 (1972), 873-890.
  • [10] D. Preiss, Metric spaces in which Prokhorov’s theorem is not valid, Z. Wahrsch. Verw. Gebiete 27 (1973), 109-116.
  • [11] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theor. Probab. Appl. 1 (1956), 157-216.
  • [12] K. K. Siggini, On the construction of set-valued measures, Bull. Polish Acad. Sci. Math. 51 (2003), 251-259.
  • [13] -, Compacité etroite des multi-applications tendues, Rev. Roumaine Math. Pures Appl. 33 (1988), 457-470.
  • [14] -, Sur la compacité des multimesures I, C. R. Math. Acad. Sci. Paris 334 (2002), 949-952.
  • [15] D. S. Thiam, Intégration dans les espaces ordonnes et integration multivoque, thèse, Univ. Pierre et Marie Curie, 1976.
  • [16] F. Topsøe, Compactness in spaces of measures, Studia Math. 36 (1970), 195-212.
  • [17] -, Topology and Measure, Lecture Notes in Math. 133, Springer, Berlin, 1970.
  • [18] V. S. Varadarajan, Measures on topological spaces, Mat. Sb. 55 (1961), 35-100 (in Russian); English transl.: Amer. Math. Soc. Transl. Ser. II 48 (1965), 161-228.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0029-0003
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