Weak Sequential Convergence in L^1(\mu,X) and an Exact Version of Fatou's Lemma
Weak Sequential Convergence in L^1(\mu,X) and an Exact Version of Fatou's Lemma
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L^1(mu,X) 中的弱顺序收敛性和 Fatou 引理的精确版本
DOI：
10.1016/j.jmaa.2013.10.082
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发表时间：
2014
影响因子：
1.3
通讯作者：
M. Ali Khan and Nobusumi Sagara
中科院分区：
文献类型：
--
作者：
Hsu;S.;M. Naoi;W. Zhang;石野卓也・瀬古美喜;岩井克人・瀬古美喜・翁百合;直井道生;Fumi Kiyotaki and Toshiji Miyakawa;若森章孝;Fumi Kiyotaki and Toshiji Miyakawa;M. Ali Khan and Nobusumi Sagara
Maharam（1942）和Hoover-Keisler（1984）发展的具有饱和性质的非原子有限测度空间类，其特征在于取值于Banach空间的良控多值函数序列的Fatou（和Lebesgue）性质。随着多功能减少到功能，这Fatou特征也延伸到一个变种的封闭性发现在最优控制理论。结果是通过考虑概述的相关文献的确切和近似的Fatou引理措辞的Bochner整合。
The class of nonatomic finite measure spaces with the saturation property, as developed in Maharam (1942) and Hoover–Keisler (1984), is characterized by the Fatou (and Lebesgue) property of a well-dominated sequence of multifunctions taking values in a Banach space. With multifunctions reduced to functions, this Fatou characterization also extends to a variant of the closure property found in optimal control theory. The results are developed through a considered overview of the relevant literature on the exact and approximate Fatou lemma phrased in terms of Bochner integration.