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Selection theorem in L¹

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Abstrakty
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Let F be a multifunction from a metric space X into L¹, and B a subset of X. We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F(x) for x ∈ B.
Twórcy
  • Silesian University, Institute of Mathematics, Bankowa 14, 40-007 Katowice, Poland
autor
  • University of Bielsko-Biała, Department of Mathematics, Willowa 2, 43-309 Bielsko-Biała, Poland
Bibliografia
  • [1] S.M. Ageev and D. Repovs, On selection theorems with decomposable values, Topol. Methods Nonlinear Anal. 15 (2000), 385-399.
  • [2] A.V. Arutyunov, Special selectors of multivalued mappings (in Russian), Dokl. Akad. Nauk Ross. Akad. Nauk 377 (3) (2001), 298-300. English translation: Dokl. Math. 63 (2) (2001), 182-184.
  • [3] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86.
  • [4] A. Fryszkowski, Continuous selections for a class of non-convex multivalued maps, Studia Math. 76 (1983), 163-174.
  • [5] F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivariate Anal. 7 (1977), 149-182.
  • [6] C.J. Himmelberg, Measurable relations, Fund. Math. 87 (1975), 53-72.
  • [7] S.J. Leese, Multifunctions of Souslin type, Bull. Austral. Math. Soc. 11 (1974), 395-411.
  • [8] A. Nowak and C. Rom, Decomposable hulls of multifunctions, Discuss. Math. Differ. Incl. Control Optim. 22 (2002), 233-241.
  • [9] Cz. Olech, Decomposability as a substitute for convexity, Multifunctions and Integrands: Stochastic Analysis, Approximation and Optimization, Proc. Conf. Catania, Italy, June 7-16, 1983 (G. Salinetti, ed.); Lecture Notes in Math., vol. 1091, Springer-Verlag, Berlin, 1984, pp. 193-205.
  • [10] A.A. Tolstonogov and D.A. Tolstonogov, Lₚ-continuous extreme selectors of multifunctions with decomposable values: Existence theorems, Set-Valued Anal. 4 (1996), 173-203.
  • [11] D.H. Wagner, Survey of measurable selection theorems, SIAM J. Control Optim. 15 (5) (1977), 859-903.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1069
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