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Based on the analysis of the stratification structure and the recently developed separation theorems in random locally convex modules, some nice basic properties about subdifferentials and approximate subdifferentials of a L 0 -valued function on random locally convex modules are obtained. The main results are as follows. First, for a proper and T c -lower semicontinuous L 0 -valued L 0 (F )-convex function f defined on a random locally convex module (E, Λ ) where both E and Λ have the countable concatenation property, it is proven that the approximate subdifferential of f is nonempty. Second, for two propers and T c -lower semicontinuous L 0 -valued L 0 (F )-convex functions, denoted by f and g , which are defined on a random locally convex module (E, Λ ) where both E and Λ have the countable concatenation property, the formula about the subdifferentials of f +g is given., authors=YANG Yujie, authorsList=YANG Yujie, authorCompany=School of Mathematics and Systems Science, Beihang University, Beijing 100191, China, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=92LH2REbu2IwRSprxdCLRA==, pdfFileSize=769618, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1242128804672504186, articleId=1242128801782628718, 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科技导报
|研究论文
2012
, 30
(12) :
50
-53
随机局部凸模上
L 0 -值函数次微分和近似次微分性质
全屏
杨玉洁
作者信息
北京航空航天大学数学与系统科学学院，北京 100191
Properties of Subdifferentials and Approximate Subdifferentials of L 0 -Valued Functions on Random Locally Convex Modules
YANG Yujie
Affiliations
School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
出版时间: 2012-04-28
doi: 10.3981/j.issn.1000-7857.2012.12.007
文章导航
研究了随机凸分析中的次微分与近似次微分问题。在层次结构分析以及最近建立的随机局部凸模上的分离定理基础上，本文得到了关于随机局部凸模上L 0 值函数的次微分和近似次微分的一些良好基本性质。首先由随机局部凸模上点与集合的分离定理，证明了：对于具有可数连结性质的随机局部凸模上真的、T c -下半连续的、L 0 (F )-凸函数，它的近似次微分非空；再者，由随机局部凸模上两个集合的分离定理，证明了对于具有可数连结性质的随机局部凸模上两个真的、T c -下半连续的、L 0 (F )-凸函数，及其次微分公式。其中，L 0 (F )表示定义在概率空间上的广义实值随机变量等价类全体形成的集合。本文推广了经典凸分析中的相应结果。
随机局部凸模
/
随机共轭空间
/
局部L 0 -凸拓扑
/
次微分
The random convex analysis of subdifferentials and approximate subdifferentials is carried out in this paper. Based on the analysis of the stratification structure and the recently developed separation theorems in random locally convex modules, some nice basic properties about subdifferentials and approximate subdifferentials of a L 0 -valued function on random locally convex modules are obtained. The main results are as follows. First, for a proper and T c -lower semicontinuous L 0 -valued L 0 (F )-convex function f defined on a random locally convex module (E, Λ ) where both E and Λ have the countable concatenation property, it is proven that the approximate subdifferential of f is nonempty. Second, for two propers and T c -lower semicontinuous L 0 -valued L 0 (F )-convex functions, denoted by f and g , which are defined on a random locally convex module (E, Λ ) where both E and Λ have the countable concatenation property, the formula about the subdifferentials of f +g is given.
random locally convex module
/
random conjugate space
/
locally L 0 -convex topology
/
subdifferential
杨玉洁.
随机局部凸模上L 0 -值函数次微分和近似次微分性质.
科技导报,
2012
, 30
(12)
: 50
-53
.
DOI: 10.3981/j.issn.1000-7857.2012.12.007
YANG Yujie.
Properties of Subdifferentials and Approximate Subdifferentials of L 0 -Valued Functions on Random Locally Convex Modules[J].
Science & Technology Review ,
2012
, 30
(12)
: 50
-53
.
DOI: 10.3981/j.issn.1000-7857.2012.12.007
2012年第30卷第12期
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文章信息
doi: 10.3981/j.issn.1000-7857.2012.12.007
接收时间：2012-02-21
首发时间：2012-04-28
出版时间：2012-04-28
收稿日期：2012-02-21
修回日期：2012-04-10
https://castjournals.cast.org.cn/joweb/kjdb/CN/10.3981/j.issn.1000-7857.2012.12.007
引用本文
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