| 基于正则收敛意义下决策函数空间的紧致性 |
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| 引用本文： | 邓书显,曹殿立.基于正则收敛意义下决策函数空间的紧致性[J].南方冶金学院学报,2009,30(1):45-48. |
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| 作者姓名： | 邓书显 曹殿立 |
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| 作者单位： | 邓书显(东华大学信息科学与技术学院,上海,201620;河南工程学院,郑州,450007);曹殿立(河南农业大学信息与管理科学学院,郑州,450002)
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| 基金项目： | 河南省基础与前沿技术研究计划 |
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| 摘 要： | 就决策函数空间的特性进行讨论，指出任何统计决策问题总是与一个随机过程有关的，所有统计决策函数所构成的集合可以看作是一个拓扑空间．在给出了决策函数的概念、正则收敛意义下收敛的定义以及权函数的概念之后，引入了决策空间的内在度量．进而运用现代泛函分析的网格理论，就离散和连续两种情况证明了决策函数空间的紧致性．为统计决策函数在现代经济分析、预测、控制等领域的应用，从理论上奠定了基础．
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| 关 键 词： | 决策函数 正则收敛 紧致性 控制 |
The Compactness of Decision-making Functional Spaces Based on the Sense of Regular Convergence |
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| DENG Shu-xian,CAO Dian-li.The Compactness of Decision-making Functional Spaces Based on the Sense of Regular Convergence[J].Journal of Southern Institute of Metallurgy,2009,30(1):45-48. |
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| Authors: | DENG Shu-xian CAO Dian-li |
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| Affiliation: | 1.College of Information Science and Technology;Donghua University;Shanghai 201620;China;2.College of Information and Management Science;Henan Agricultural University;Zhengzhou 450002;3.Henan Engineering College;Zhengzhou 450007;China |
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| Abstract: | In this paper, the characteristic of decision-making functional spaces is discussed.All statistical decision-making problems are related to a series of random courses.The set made up of all statistical decision-makingfunctions can be treated as a topology space.After the definition of decision-making functions, convergence on thesense of regular convergence and weight functions are presented, the intrinsic measurement in decision-makingspaces are introduced.Then the mesh theory in modern functional analysis... |
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| Keywords: | decision-making function regular convergence compactness control |
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