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.
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Castaing, C., Saadoune, M. (2009). Convergences in a dual space with applications to Fatou lemma. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advance in Mathematical Economics, vol 12. Springer, Tokyo. https://doi.org/10.1007/978-4-431-92935-2_2
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DOI: https://doi.org/10.1007/978-4-431-92935-2_2
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