Adv. Math. Econ. 12, 23-69 (2009)

Convergences in a dual space with applications to Fatou lemma

Charles Castaing^{1} and Mohamed Saadoune^{2}

1 Département de Mathématiques, Université Montpellier II, Place E. Bataillon, 34095 Montpellier cedex, France

2 Département de Mathématiques, Université Ibn Zohr, Lot. Addakhla, B.P. 8106, Agadir, Marocco

Received: July 27, 2008 Revised: September 9, 2008

JEL classification: C01, C02, C62

Mathematical Subject Classification (2000): 29B20, 28A20

Abstract. We present new convergence results and new versions of Fatou lemma in Mathematical Economics based on various tightness conditions and the existence of scalarly integrable selections theorems for the (sequential)-weak-star upper limit of a sequence of measurable multifunctions taking values in the dual E of a separable Banach space E. Existence of conditional expectation of weakly-star closed random sets in a non norm separable dual space is also provided.

Key words: Biting lemma, conditional expectation, Fatou lemma, Komlós convergence, sequential weak upper limit, Tightness