Abstract
We prove various results for the conditional expectation of multifunctions and normal integrands. Applications to the epiconvergence of integrand reversed martingales and lower semicontinuous superadditive random sequences are presented.
Received: October 4, 2010
Revised: October 25, 2010
JEL classification: C01, C02
Mathematics Subject Classification (2010): 28B20, 60G42, 46A17, 54A20
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Notes
- 1.
For more consideration on the finiteness or continuity assumption of \({I}_{{f}^{{_\ast}}}(u) := \int \nolimits _{\Omega }{f}^{{_\ast}}(\omega,u(\omega )){\it { dP}}(\omega )\) on \({L}_{E}^{\infty }(\Omega,\mathcal{F},P)\), see [5], Chap. VIII.
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Castaing, C. (2011). Some various convergence results for normal integrands. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 15. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53930-8_1
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