Abstract
Let E be a separable super reflexive Banach space and let \( \left( {\Omega ,\mathcal{F}{\text{,}}\mu } \right) \) be a complete probability space. We state some Komlós type theorems in the space \( \mathcal{L}_E^{\text{0}} \left( {\Omega ,\mathcal{F}{\text{,}}\mu } \right) \) of E-valued random variables and a version of Komlós slice theorem in the space \( \mathcal{L}_{cwk\left( E \right)}^{\text{0}} \left( {\Omega ,\mathcal{F},\mu } \right) \) of convex weakly compact random sets. Weak Komlós type theorems for some unbounded sequences in \( \mathcal{L}_F^{\text{1}} \left( {\Omega ,\mathcal{F},\mu } \right){\mathbf{ }}{\text{and}}{\mathbf{ }}\mathcal{L}_F^{\text{1}} \left[ F \right]\left( {\Omega ,\mathcal{F},\mu } \right) \) when F is a separable Banach space are also stated. A Fatou type lemma in Mathematical Economics and minimization problems on convex and closed in measure subsets of \( \mathcal{L}_E^{\text{0}} \left( {\Omega ,\mathcal{F},\mu } \right) \) are presented. Further Minimization problems and Min-Max type results involving saddle-points and Young measures are also investigated.
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Castaing, C., Saadoune, M. (2007). Komlós type convergence for random variables and random sets with applications to minimization problems. In: Kusuoka, S., Yamazaki, A. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 10. Springer, Tokyo. https://doi.org/10.1007/978-4-431-72761-3_1
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