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REPRESENTATION THEOREMS FOR MULTIVALUED PRAMARTS
Akhiat, Fettah,Ezzaki, Fatima Korean Mathematical Society 2013 대한수학회지 Vol.50 No.1
Existence of pramarts selectors for multivalued pramart whose values are convex weakly compact subsets of a separable Banach space E (resp. subsets of a dual space $E^*$) are established. Representation theorems for multivalued pramarts are also presented.
Representation theorems for multivalued pramarts
Fettah Akhiat,Fatima Ezzaki 대한수학회 2013 대한수학회지 Vol.50 No.1
Existence of pramarts selectors for multivalued pramart whose values are convex weakly compact subsets of a separable Banach space E (resp. subsets of a dual space E*) are established. Representation theorems for multivalued pramarts are also presented.
PETTIS CONDITIONAL EXPECTATION OF CLOSED CONVEX RANDOM SETS IN A BANACH SPACE WITHOUT RNP
Akhiat, Fattah,El Harami, Mohamed,Ezzaki, Fatima Korean Mathematical Society 2018 대한수학회지 Vol.55 No.4
In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued $L{\acute{e}}vy^{\prime}s$ martingale convergence theorem for integrable and Pettis integrable random sets are proved.
Pettis conditional expectation of closed convex random sets in a Banach space without $RNP$
Fattah Akhiat,Mohamed El Harami,Fatima Ezzaki 대한수학회 2018 대한수학회지 Vol.55 No.4
In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued L\'evy's martingale convergence theorem for integrable and Pettis integrable random sets are proved.