Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Single-valued representation of set-valued mappings

Author: A. D. Ioffe
Journal: Trans. Amer. Math. Soc. 252 (1979), 133-145
MSC: Primary 28B20; Secondary 54C65
MathSciNet review: 534114
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the graph of a set-valued mapping satisfying typical conditions which guarantee the existence of measurable selections can be represented as the union of graphs of measurable single-valued mappings depending continuously on a parameter running through some Polish space.

References [Enhancements On Off] (What's this?)

  • [1] Robert J. Aumann, Measurable utility and the measurable choice theorem, La Décision, 2: Agrégation et Dynamique des Ordres de Préférence (Actes Colloq. Internat., Aix-en-Provence, 1967) Éditions du Centre Nat. Recherche Sci., Paris, 1969, pp. 15–26 (English, with French summary). MR 0261938
  • [2] D. W. Bressler and M. Sion, The current theory of analytic sets, Canad. J. Math. 16 (1964), 207–230. MR 0163854
  • [3] Ch. Castaing, Sur les multi-applications mesurables, Rev. Française Informat. Recherche Opérationnell 1 (1967), no. 1, 91–126 (French). MR 0223527
  • [4] Claude Dellacherie and Paul-André Meyer, Probabilités et potentiel, Hermann, Paris, 1975 (French). Chapitres I à IV; Édition entièrement refondue; Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. XV; Actualités Scientifiques et Industrielles, No. 1372. MR 0488194
  • [5] J. Hoffmann-Jørgensen, The theory of analytic spaces, Matematisk Institut, Aarhus Universitet, Aarhus, 1970. Various Publication Series, No. 10. MR 0409748
  • [6] Alexander D. Ioffe, Representation theorems for multifunctions and analytic sets, Bull. Amer. Math. Soc. 84 (1978), no. 1, 142–144. MR 0466472, 10.1090/S0002-9904-1978-14444-9
  • [7] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
  • [8] K. Kuratowski and C. Ryll-Nardzewski, A general theorem on selectors, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 397–403 (English, with Russian summary). MR 0188994
  • [9] S. J. Leese, Multifunctions of Souslin type, Bull. Austral. Math. Soc. 11 (1974), 395–411. MR 0417365
  • [10] S. J. Leese, Measurable selections and the uniformization of Souslin sets, Amer. J. Math. 100 (1978), no. 1, 19–41. MR 0507445
  • [11] V. L. Levin, Subdifferentials and continuous extensions preserving measurable dependence on a parameter, Funkcional. Anal. i Priložen. 10 (1976), no. 3, 84–85 (Russian). MR 0423073
  • [12] P. S. Novikov, On projections of certain B-sets, Dokl. Akad. Nauk SSSR 23 (1939), 863-866.
  • [13] V. A. Rokhlin, Selected topics from the metric theory of dynamical systems, Amer. Math. Soc. Transl. 49 (1966), 171-240.
  • [14] J. Saint-Pierre, Charactérisation des \cal𝐹-sousliniens d’un produit et théorèmes de sections, Travaux Sém. Anal. Convexe 7 (1977), no. 2, Exp. No. 8, 46 (French). MR 0486388
  • [15] S. Simons, A proof that 𝑆𝑜𝑢𝑠𝑙𝑖𝑛𝑆𝑜𝑢𝑠𝑙𝑖𝑛𝐻⊂𝑆𝑜𝑢𝑠𝑙𝑖𝑛𝐻, Canad. Math. Bull. 9 (1966), 79–82. MR 0200164

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 28B20, 54C65

Retrieve articles in all journals with MSC: 28B20, 54C65

Additional Information

Article copyright: © Copyright 1979 American Mathematical Society