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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.
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참고문헌 (26)
참고문헌 신청
F. Akhiat / 2010 / Some various convergence results for multivalued martingales, in Advances in mathematical economics. Volume 13 / Springer :1~33
A. Amrani / 1997 / Weak compactness in Pettis integration / Bull. Pol. Acad. Sci. Math. 45(2):139~150
A. Amrani / 1998 / Convergence in Pettis norm under extreme point condition / Vietnam J. Math. 26(4):323~335
I. Assani / 1982 / Parties decomposables compactes de $L^1_E$ / 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
A. Amrani / 1997 / Weak compactness in Pettis integration / Bull. Pol. Acad. Sci. Math. 45(2):139~150
A. Amrani / 1998 / Convergence in Pettis norm under extreme point condition / Vietnam J. Math. 26(4):323~335
I. Assani / 1982 / Parties decomposables compactes de
G. Beer / 1989 / Support and distance functionals for convex sets / Numer. Funct. Anal. Optim. 10(1-2):15~36
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