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Journal of Convex Analysis 12 (2005), No. 2, 383--395
Copyright Heldermann Verlag 2005



Fatou's Lemma for Multifunctions with Unbounded Values in a Dual Space

Erik J. Balder
Mathematical Institute, University of Utrecht, Budapestlaan 6, 3508 TA Utrecht, The Netherlands
balder@math.uu.nl

Anna Rita Sambucini
Dip. di Matematica e Informatica, UniversitÓ di Perugia, Italy
matears1@unipg.it



A version of Fatou's lemma for multifunctions with unbounded values in infinite dimensions is presented. It generalizes both the recent Fatou-type results for Gelfand integrable functions of B. Cornet and V. F. Martins da Rocha ["Fatou's lemma for unbounded Gelfand integrable mappings", preprint 109, CERMSEM, UniversitÚ Paris I (2002)] and, in the case of finite dimensions, the finite-dimensional version of the unifying multivalued Fatou-type result of E. J. Balder and C. Hess [Math. Oper. Res. 20 (1995) 175--188].

Keywords: Fatou's lemma in several dimensions, Gelfand integral, Young measure, asymptotic cone.

MSC: 29B20; 28A20

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