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In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued L\'evy's martingale convergence theorem are proved by using the Slice and the linear topologies.
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참고문헌 (28)
참고문헌 신청
F. Akhiat / 2010 / Some various convergence results for multival-ued martingales / Advances in Mathematical Economics 13:1~33
Fattah Akhiat / 2018 / Pettis conditional expectation of closed convex random sets in a Banach space without $RNP$ / 대한수학회지 55(4):833~848
A. Amrani / 1997 / Weak compactness in Pettis integration / Bull. Polish Acad. Sci. Math 45(2):139~150
I. Assani / 1982 / Parties decomposables compactes de L1E / C. R. Acad. Sci. Paris Ser. I Math 294(16):533~536
G. Beer / 1989 / Support and distance functionals for convex sets / Numer. Funct. Anal. Optim 10(1-2):15~36
Fattah Akhiat / 2018 / Pettis conditional expectation of closed convex random sets in a Banach space without $RNP$ / 대한수학회지 55(4):833~848
A. Amrani / 1997 / Weak compactness in Pettis integration / Bull. Polish Acad. Sci. Math 45(2):139~150
I. Assani / 1982 / Parties decomposables compactes de L1E / C. R. Acad. Sci. Paris Ser. I Math 294(16):533~536
G. Beer / 1989 / Support and distance functionals for convex sets / Numer. Funct. Anal. Optim 10(1-2):15~36
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