| 集值下鞅的一类Riesz分解 |
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| 引用本文： | 李高明,李海鹏.集值下鞅的一类Riesz分解[J].吉林大学学报(理学版),2011,49(6):1039-1043. |
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| 作者姓名： | 李高明 李海鹏 |
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| 作者单位： | 1. 武警工程大学 理学院, 西安 710086； 2. 西安电子工程研究所, 西安 710100 |
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| 基金项目： | 陕西省自然科学基金(批准号:SJ08A28); 武警工程学院基础研究项目基金(批准号:WJY201007) |
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| 摘 要： | 举例说明即使在一维实空间, 集值下鞅并非都可Riesz分解, 即集值下鞅表示为集值鞅与集值下鞅之和. 给出集值下鞅一种新的Riesz分解定义, 证明了一维实空间集值下鞅有该种形式的Riesz分解, 并举例说明在二维实空间, 集值下鞅不具有这种形式的Riesz分解. 最后证明了集值下鞅具有这种形式Riesz分解的充分必要条件.
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| 关 键 词： | 集值（下）鞅 Kuratowski Mosco收敛 Riesz分解 支撑函数 |
| 收稿时间： | 2011-03-30 |
A Class of Riesz Decomposition for Set-Valued Submartingle |
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| LI Gao-ming,LI Hai-peng.A Class of Riesz Decomposition for Set-Valued Submartingle[J].Journal of Jilin University: Sci Ed,2011,49(6):1039-1043. |
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| Authors: | LI Gao-ming LI Hai-peng |
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| Institution: | 1. College of Science, Engineering University of Armed Police Force, Xi’an 710086, China;2. Xi’an Electronic Engineering Research Institute, Xi’an 710100, China |
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| Abstract: | Some certain examples were mentioned in order to prove that not all the set-valued submartingle could be decomposed even in one dimension real space.In other words,the set-valued submartingle means the sum of set-valued martingle and set-valued submartingle.A new definition about the Riesz decomposition of set-valued submartingle was presented.We proved that the set-valued submartingle possesses the new form of definition in one dimension real space.In order to illustrate that the new definition is not avai... |
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| Keywords: | set-valued(sub) martingale Kuratowski-Mosco convergence Riesz decomposition support function |
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