Single-valued representation of set-valued mappings

Ioffe, A. D.

doi:10.1090/S0002-9947-1979-0534114-6

Single-valued representation of set-valued mappings
HTML articles powered by AMS MathViewer

by A. D. Ioffe PDF

Trans. Amer. Math. Soc. 252 (1979), 133-145 Request permission

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

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 National de la Recherche Scientifique (CNRS), Paris, 1969, pp. 15–26 (English, with French summary). MR 0261938
D. W. Bressler and M. Sion, The current theory of analytic sets, Canadian J. Math. 16 (1964), 207–230. MR 163854, DOI 10.4153/CJM-1964-021-7
Ch. Castaing, Sur les multi-applications mesurables, Rev. Française Informat. Recherche Opérationnell 1 (1967), no. 1, 91–126 (French). MR 0223527
Claude Dellacherie and Paul-André Meyer, Probabilités et potentiel, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. XV, Hermann, Paris, 1975 (French). Chapitres I à IV; Édition entièrement refondue. MR 0488194
J. Hoffmann-Jørgensen, The theory of analytic spaces, Various Publications Series, No. 10, Aarhus Universitet, Matematisk Institut, Aarhus, 1970. MR 0409748
Alexander D. Ioffe, Representation theorems for multifunctions and analytic sets, Bull. Amer. Math. Soc. 84 (1978), no. 1, 142–144. MR 466472, DOI 10.1090/S0002-9904-1978-14444-9
K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
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 188994
S. J. Leese, Multifunctions of Souslin type, Bull. Austral. Math. Soc. 11 (1974), 395–411. MR 417365, DOI 10.1017/S0004972700044038
S. J. Leese, Measurable selections and the uniformization of Souslin sets, Amer. J. Math. 100 (1978), no. 1, 19–41. MR 507445, DOI 10.2307/2373874
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

On projections of certain B-sets

23

Selected topics from the metric theory of dynamical systems

49

J. Saint-Pierre, Charactérisation des ${\cal F}$-sousliniens d’un produit et théorèmes de sections, Travaux Sém. Anal. Convexe 7 (1977), no. 2, Exp. No. 8, 46 (French). MR 486388
S. Simons, A proof that $\textrm {Souslin\ Souslin}\ H\subset \ \textrm {Souslin}\ H$, Canad. Math. Bull. 9 (1966), 79–82. MR 200164, DOI 10.4153/CMB-1966-010-6