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

Erik J. Balder; Anna Rita Sambucini

Abstract

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, Université 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].

Author information

Contact details are reproduced from the original publication and may be historical.

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, Università di Perugia, Italy

matears1@unipg.it

Keywords

Fatou's lemma in several dimensions
Gelfand integral
Young measure
asymptotic cone

Mathematics Subject Classification

29B20; 28A20

Suggested citation

E. J. Balder, A. R. Sambucini. “Fatou's Lemma for Multifunctions with Unbounded Values in a Dual Space.” Journal of Convex Analysis 12 (2005), No. 2, 383–395.