On the Riesz Integral Representation of Additives Set-Valued Maps (I)

Lakmon Kodjovi, S. Kenny, Ayassou Emmanuel, Tchariè Kokou
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Abstract

In this paper we generalize the Riesz integral representation for continuous linear maps associated with additive set-valued maps with values in the set of all closed bounded convex non-empty subsets of any Banach space. We deduce the Riesz integral representation results for set-valued maps, for vector-valued maps of Diestel-Uhl and for scalar-valued maps of Dunford-Schwartz.
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关于附加集值映射的Riesz积分表示(I)
本文推广了连续线性映射与加性集值映射相关的Riesz积分表示,其值在任意Banach空间的所有闭有界凸非空子集的集合中。我们推导了集合值映射、Diestel-Uhl的向量值映射和Dunford-Schwartz的标量值映射的Riesz积分表示结果。
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